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分类：生物统计代写

统计代写|生物统计代写biostatistics代考|MPH701

Posted on 2022年6月28日2022年6月28日 by statistics-lab

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生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

statistics-lab™ 为您的留学生涯保驾护航在代写生物统计biostatistics方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写生物统计biostatistics代写方面经验极为丰富，各种生物统计biostatistics相关的作业也就用不着说。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|Extension to the Regression Case

We want to extend the methodology of Sect. $3.2$ to the regression setting where the location parameter varies across observations as a linear function of a set of $p$, say, explanatory variables, which are assumed to include the constant term, as it is commonly the case. If $x_{i}$ is the vector of covariates pertaining to the $i$ th subject, observation $y_{i}$ is now assumed to be drawn from ST $\left(\xi_{i}, \omega, \lambda, \nu\right)$ where
$$
\xi_{i}=x_{i}^{\top} \beta, \quad i=1, \ldots, n,
$$
for some $p$-dimensional vector $\beta$ of unknown parameters; hence now the parameter vector is $\theta=\left(\beta^{\top}, \omega, \lambda, v\right)^{\top}$. The assumption of independently drawn observations is retained.

The direct extension of the median as an estimate of location, which was used in Sect. 3.2, is an estimate of $\beta$ obtained by median regression, which corresponds to adoption of the least absolute deviations fitting criterion instead of the more familiar least squares. This can also be viewed as a special case of quantile regression, when the quantile level is set at $1 / 2$. A classical treatment of quantile regression

is Koenker (2005) and corresponding numerical work can be carried out using the $R$ package quantreg, see Koenker (2018), among other tools.

Use of median regression delivers an estimate $\tilde{\tilde{\beta}}^{m}$ of $\beta$ and a vector of residual values, $r_{i}=y_{i}-x_{i}^{\top} \tilde{\beta}^{m}$ for $i=1, \ldots, n$. Ignoring $\beta$ estimation errors, these residuals are values sampled from $\mathrm{ST}\left(-m_{0}, \omega^{2}, \lambda, v\right)$, where $m_{0}$ is a suitable value, examined shortly, which makes the distribution to have 0 median, since this is the target of the median regression criterion. We can then use the same procedure of Sect. 3.2, with the $y_{i}$ ‘s replaced the $r_{i}$ ‘s, to estimate $\omega, \lambda, v$, given that the value of $m_{0}$ is irrelevant at this stage.

The final step is a correction to the vector $\tilde{\beta}^{m}$ to adjust for the fact that $y_{i}-x_{i}^{\top} \beta$ should have median $m_{0}$, that is, the median of ST $(0, \omega, \lambda, v)$, not median 0 . This amounts to increase all residuals by a constant value $m_{0}$, and this step is accoomplishéd by sêtting a vectoor $\tilde{\beta}$ with all components equal tō $\tilde{\beta}^{m}$ except that the intercept term, $\beta_{0}$ say, is estimated by
$$
\tilde{\beta}{0}=\tilde{\beta}{0}^{m}-\tilde{\omega} q_{2}^{\mathrm{ST}}
$$
similarly to $(10)$

统计代写|生物统计代写biostatistics代考|Extension to the Multivariate Case

Consider now the case of $n$ independent observations from a multivariate $Y$ variable with density (6), hence $Y \sim \mathrm{ST}{d}(\xi, \Omega, \alpha, v)$. This case can be combined with the regression setting of Sect. 3.3, so that the $d$-dimensional location parameter varies for each observation according to $$ \xi{i}^{\top}=x_{i}^{\top} \beta, \quad i=1, \ldots, n,
$$
where now $\beta=\left(\beta_{\cdot 1}, \ldots, \beta_{\cdot d}\right)$ is a $p \times d$ matrix of parameters. Since we have assumed that the explanatory variables include a constant term, the regression case subsumes the one of identical distribution, when $p=1$. Hence we deal with the regression case directly, where the $i$ th observation is sampled from $Y_{i} \sim$ $\mathrm{ST}{d}\left(\xi{i}, \Omega, \alpha, v\right)$ and $\xi_{i}$ is given by (12), for $i=1, \ldots, n$.

Arrange the observed values in a $n \times d$ matrix $y=\left(y_{i j}\right)$. Application of the procedure presented in Sects. $3.2$ and $3.3$ separately to each column of $y$ delivers estimates of $d$ univariate models. Specifically, from the $j$ th column of $y$, we obtain estimates $\tilde{\theta}{j}$ and corresponding ‘normalized’ residuals $\tilde{z}{i j}$ :
$$
\tilde{\theta}{j}=\left(\tilde{\beta}{\cdot j}^{\top}, \tilde{\omega}{j}, \tilde{\lambda}{j}, \tilde{v}{j}\right)^{\top}, \quad \tilde{z}{i j}=\tilde{\omega}{j}^{-1}\left(y{i j}-x_{i}^{\top} \tilde{\beta}_{\cdot j}\right)
$$

where it must be recalled that the ‘normalization’ operation uses location and scale parameters, but these do not coincide with the mean and the standard deviation of the underlying random variable.

Since the meaning of expression (12) is to define a set of univariate regression modes with a common design matrix, the vectors $\tilde{\beta}{-1}, \ldots, \tilde{\beta}{\cdot d}$ can simply be arranged in a $p \times d$ matrix $\tilde{\beta}$ which represents an estimate of $\beta$.

The set of univariate estimates in (13) provide $d$ estimates for $v$, while only one such a value enters the specification of the multivariate ST distribution. We have adopted the median of $\tilde{v}{1}, \ldots, \tilde{v}{d}$ as the single required estimate, denoted $\tilde{v}$.

The scale quantities $\tilde{\omega}{1}, \ldots, \tilde{\omega}{d}$ estimate the square roots of the diagonal elements of $\Omega$, but off-diagonal elements require a separate estimation step. What is really required to estimate is the scale-free matrix $\bar{\Omega}$. This is the problem examined next.

If $\omega$ is the diagonal matrix formed by the squares roots of $\Omega_{11}, \ldots, \Omega_{\text {cld }}$, all variables $\omega^{-1}\left(Y_{i}-\xi_{i}\right)$ have distribution $\mathrm{ST}{d}(0, \bar{\Omega}, \alpha, v)$, for $i=1, \ldots, n$. Denote by $Z=\left(Z{1}, \ldots, Z_{d}\right)^{\top}$ the generic member of this set of variables. We are concerned with the distribution of the products $Z_{j} Z_{k}$, but for notational simplicity we focus on the specific product $W=Z_{1} Z_{2}$, since all other products are of similar nature.

We must then examine the distribution of $W=Z_{1} Z_{2}$ when $\left(Z_{1}, Z_{2}\right)$ is a bivariate ST variable. This looks at first to be a daunting task, but a major simplification is provided by consideration of the perturbation invariance property of symmetrymodulated distributions, of which the ST is an instance. For a precise exposition of this property, see for instance Proposition $1.4$ of Azzalini and Capitanio (2014), but in the present case it says that, since $W$ is an even function of $\left(Z_{1}, Z_{2}\right)$, its distribution does not depend on $\alpha$, and it coincides with the distribution of the case $\alpha=0$, that is, the case of a usual bivariate Student’s $t$ distribution, with dependence parameter $\bar{\Omega}_{12}$.

统计代写|生物统计代写biostatistics代考|Simulation Work to Compare Initialization Procedures

Several simulations runs have been performed to examine the performance of the proposed methodology. The computing environment was $\mathrm{R}$ version 3.6.0. The reference point for these evaluations is the methodology currently in use, as provided by the publicly available version of $R$ package $s n$ at the time of writing, namely version 1.5-4; see Azzalini (2019). This will be denoted ‘the current method’ in the following. Since the role of the proposed method is to initialize the numerical MLE search, not the initialization procedure per se, we compare the new and the current method with respect to final MLE outcome. However, since the numerical optimization method used after initialization is the same, any variations in the results originate from the different initialization procedures.

We stress again that in a vast number of cases the working of the current method is satisfactory and we are aiming at improvements when dealing with ‘awkward samples’. These commonly arise with ST distributions having low degrees of freedom, about $v=1$ or even less, but exceptions exist, such as the second sample in Fig. $2 .$

The primary aspect of interest is improvement in the quality of data fitting. This is typically expressed as an increase of the maximal achieved log-likelihood, in its penalized form. Another desirable effect is improvement in computing time.

The basic set-up for such numerical experiments is represented by simple random samples, obtained as independent and identically distributed values drawn from a named ST $(\xi, \omega, \lambda, v)$. In all cases we set $\xi=0$ and $\omega=1$. For the other ingredients, we have selected the following values:
$\lambda: 0, \quad 2, \quad 8$,
$v: 1,3,8$,
$n: 50,100,250,500$
and, for each combination of these values, $N=2000$ samples have been drawn.
The smallest examined sample size, $n=50$, must be regarded as a sort of ‘sensible lower bound’ for realistic fitting of flexible distributions such as the ST. In this respect, recall the cautionary note of Azzalini and Capitanio (2014, p. 63) about the fitting of a SN distribution with small sample sizes. Since the ST involves an additional parameter, notably one having a strong effect on tail behaviour, that annotation holds a fortiori here.

For each of the $3 \times 3 \times 4 \times 2000=72,000$ samples so generated, estimation of the parameters $(\xi, \omega, \lambda, \nu)$ has been carried out using the following methods.

生物统计代考

统计代写|生物统计代写biostatistics代考|Extension to the Regression Case

我们想扩展 Sect 的方法论。3.2回归设置，其中位置参数随观测值变化，作为一组线性函数p，比如说，假设包括常数项的解释变量，因为它通常是这种情况。如果X一世是与一世主题，观察是一世现在假设从 ST 中提取(X一世,ω,λ,ν)在哪里

X一世=X一世⊤b,一世=1,…,n,
对于一些p维向量b未知参数；因此现在参数向量是θ=(b⊤,ω,λ,在)⊤. 保留独立绘制观察的假设。

中值的直接扩展作为位置的估计，在 Sect. 3.2，是一个估计b通过中值回归获得，这对应于采用最小绝对偏差拟合标准而不是更熟悉的最小二乘法。当分位数水平设置为1/2. 分位数回归的经典处理

是 Koenker (2005)，相应的数值工作可以使用Rquantreg 包，请参阅 Koenker (2018) 等工具。

使用中值回归提供估计b~~米的b和一个残差向量，r一世=是一世−X一世⊤b~米为了一世=1,…,n. 忽略b估计误差，这些残差是从小号吨(−米0,ω2,λ,在)，在哪里米0是一个合适的值，很快就会检查，这使得分布的中位数为 0，因为这是中位数回归标准的目标。然后我们可以使用 Sect 的相同程序。3.2，与是一世取代了r一世的，估计ω,λ,在，给定的值米0在这个阶段是无关紧要的。

最后一步是对向量的修正b~米调整的事实是一世−X一世⊤b应该有中位数米0，即 ST 的中位数(0,ω,λ,在)，而不是中位数 0 。这相当于将所有残差增加一个恒定值米0, 这一步是通过设置一个向量来完成的b~所有组件都等于 tōb~米除了截距项，b0说，估计是

b~0=b~0米−ω~q2小号吨
类似于(10)

统计代写|生物统计代写biostatistics代考|Extension to the Multivariate Case

现在考虑以下情况n来自多变量的独立观察是随密度 (6) 变化，因此是∼小号吨d(X,Ω,一个,在). 这种情况可以结合Sect的回归设置。3.3，因此d- 维位置参数根据每个观察值变化

X一世⊤=X一世⊤b,一世=1,…,n,
现在在哪里b=(b⋅1,…,b⋅d)是一个p×d参数矩阵。由于我们假设解释变量包括一个常数项，回归情况包含相同分布的情况，当p=1. 因此，我们直接处理回归情况，其中一世第一次观察是从是一世∼ 小号吨d(X一世,Ω,一个,在)和X一世由 (12) 给出，对于一世=1,…,n.

将观测值排列在一个n×d矩阵是=(是一世j). 应用程序中介绍的部分。3.2和3.3分别到每一列是提供估计d单变量模型。具体来说，从j第列是, 我们得到估计θ~j和相应的“归一化”残差和~一世j :

θ~j=(b~⋅j⊤,ω~j,λ~j,在~j)⊤,和~一世j=ω~j−1(是一世j−X一世⊤b~⋅j)

必须记住，“归一化”操作使用位置和尺度参数，但这些参数与基础随机变量的均值和标准差不一致。

由于表达式 (12) 的含义是定义一组具有共同设计矩阵的单变量回归模式，因此向量b~−1,…,b~⋅d可以简单地排列成一个p×d矩阵b~这代表了一个估计b.

（13）中的一组单变量估计提供d估计为在，而只有一个这样的值进入多元 ST 分布的规范。我们采用了 $\tilde{v} {1}、\ldots、\tilde{v} {d}的中位数一个s吨H和s一世nGl和r和q在一世r和d和s吨一世米一个吨和,d和n○吨和d\波浪号 {v} $。

规模数量ω~1,…,ω~d估计对角线元素的平方根Ω，但非对角线元素需要单独的估计步骤。真正需要估计的是无标度矩阵Ω¯. 这是接下来要研究的问题。

如果ω是由的平方根形成的对角矩阵Ω11,…,Ω分类 , 所有变量ω−1(是一世−X一世)有分布小号吨d(0,Ω¯,一个,在)，为了一世=1,…,n. 表示为从=(从1,…,从d)⊤这组变量的通用成员。我们关心产品的分销从j从ķ，但为了符号的简单性，我们专注于特定的产品在=从1从2，因为所有其他产品都具有相似的性质。

然后我们必须检查分布在=从1从2什么时候(从1,从2)是一个二元 ST 变量。起初这看起来是一项艰巨的任务，但考虑到对称调制分布的扰动不变性特性，提供了一个主要的简化，ST 就是其中的一个例子。有关此属性的精确说明，请参见例如 Proposition1.4Azzalini 和 Capitanio (2014)，但在目前的情况下，它说，因为在是一个偶函数(从1,从2), 它的分布不依赖于一个，并且与案例的分布相吻合一个=0，即通常的双变量学生的情况吨分布，具有依赖参数Ω¯12.

统计代写|生物统计代写biostatistics代考|Simulation Work to Compare Initialization Procedures

已经进行了几次模拟运行以检查所提出的方法的性能。计算环境是R版本 3.6.0。这些评估的参考点是当前使用的方法，由公开版本提供R包裹sn在撰写本文时，即版本 1.5-4；见阿扎里尼 (2019)。这将在下文中表示为“当前方法”。由于所提出方法的作用是初始化数值 MLE 搜索，而不是初始化过程本身，我们比较新方法和当前方法的最终 MLE 结果。但是，由于初始化后使用的数值优化方法是相同的，因此结果的任何变化都源于不同的初始化程序。

我们再次强调，在大量情况下，当前方法的工作是令人满意的，我们的目标是在处理“尴尬样本”时进行改进。这些通常出现在具有低自由度的 ST 分布中，大约在=1甚至更少，但也有例外，例如图 2 中的第二个示例。2.

感兴趣的主要方面是数据拟合质量的改进。这通常以惩罚形式表示为最大实现对数似然的增加。另一个理想的效果是计算时间的改进。

此类数值实验的基本设置由简单的随机样本表示，这些样本是从命名的 ST 中提取的独立且同分布的值(X,ω,λ,在). 在所有情况下，我们设置X=0和ω=1. 对于其他成分，我们选择了以下值：
λ:0,2,8,
在:1,3,8,
n:50,100,250,500
并且，对于这些值的每种组合，ñ=2000样本已抽取。
最小的检查样本量，n=50, 必须被视为一种“合理的下界”，用于实际拟合灵活分布（例如 ST）。在这方面，回想一下 Azzalini 和 Capitanio (2014, p. 63) 关于在小样本量下拟合 SN 分布的警告说明。由于 ST 涉及一个附加参数，尤其是对尾部行为有强烈影响的参数，因此该注释在这里更重要。

对于每一个3×3×4×2000=72,000这样生成的样本，参数的估计(X,ω,λ,ν)已使用以下方法进行。

统计代写|生物统计代写biostatistics代考请认准statistics-lab™

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金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题，以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语广义线性模型（GLM）通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归，以及方差分析和方差分析（仅含固定效应）。

有限元方法代写

有限元方法（FEM）是一种流行的方法，用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法，用于解决两个或三个空间变量的偏微分方程（即一些边界值问题）。为了解决一个问题，有限元将一个大系统细分为更小、更简单的部分，称为有限元。这是通过在空间维度上的特定空间离散化来实现的，它是通过构建对象的网格来实现的：用于求解的数值域，它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统，以模拟整个问题。然后，有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写

随机微积分是数学的一个分支，对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程，是依赖于参数的一组随机变量的全体，参数通常是时间。随机变量是随机现象的数量表现，其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值（如1秒，5分钟，12小时，7天，1年），因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中，往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录，以得到其自身发展的规律。

回归分析代写

多元回归分析渐进（Multiple Regression Analysis Asymptotics）属于计量经济学领域，主要是一种数学上的统计分析方法，可以分析复杂情况下各影响因素的数学关系，在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习和应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|STA 310

Posted on 2022年6月28日2022年6月28日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|Numerical Aspects and Some Illustrations

Since, on the computational side, we shall base our work the R package sn, described by Azzalini (2019), it is appropriate to describe some key aspects of this package. There exists a comprehensive function for model fitting, called selm, but the actual numerical work in case of an ST model is performed by functions st. mple and mst. mple, in the univariate and the multivariate case, respectively. To numerical efficiency, we shall be using these functions directly, rather than via selm. As their names suggest, st. mple and mst. mple perform MPLE, but they can be used for classical MLE as well, just by omitting the penalty function. The rest of the description refers to st. mple, but mst. mple follows a similar scheme.
In the univariate case, denote by $\theta=(\xi, \omega, \alpha, \nu)^{\top}$ the parameters to be cstimatcd, or possibly $\theta=\left(\beta^{\top}, w, \alpha, v\right)^{\top}$ when a lincar regrcssion mudel is introduced for the location parameter, in which case $\beta$ is a vector of $p$ regression coefficients. Denote by $\log L(\theta)$ the log-likelihood function at point $\theta$. If no starting values are supplied, the first operation of st.mple is to fit a linear model to the available explanatory variables; this reduces to the constant covariate value 1 if $p=1$. For the residuals from this linear fit, sample cumulants of order up to four are computed, hence including the sample variance. An inversion from these

values to $\theta$ may or may not be possible, depending on whether the third and fourth sample cumulants fall in the feasible region for the ST family. If the inversion is successful, initial values of the parameters are so obtained; if not, the final two components of $\theta$ are set at $(\alpha, v)=(0,10)$, retaining the other components from the linear fit. Starting from this point, MLE or MPLE is searched for using a general numerical optimization procedure. The default procedure for performing this step is the $\mathrm{R}$ function nlminb, supplied with the score functions besides the log-likelihood function. We shall refer, comprehensively, to this currently standard procedure as ‘method M0’.

In all our numerical work, method M0 uses st. mple, and the involved function nlminb, with all tuning parameters kept at their default values. The only activated option is the one switching between MPLE and MLE, and even this only for the work of the present section. Later on, we shall always use MPLE, with penalty function Openalty which implements the method proposed in Azzalini and Arellano-Valle (2013).

We start our numerical work with some illustrations, essentially in graphical form, of the log-likelihood generated by some simulated datasets. The aim is to provide a direct perception, although inevitably limited, of the possible behaviour of the log-likelihood and the ensuing problems which it poses for MLE search and other inferential procedures. Given this aim, we focus on cases which are unusual, in some way or another, rather than on ‘plain cases’.

The type of graphical display which we adopt is based on the profile loglikelihood function of $(\alpha, v)$, denoted $\log L_{p}(\alpha, v)$. This is obtained, for any given $(\alpha, v)$, by maximizing $\log L(\theta)$ with respect to the remaining parameters. To simplify readability, we transform $\log L_{p}(\alpha, v)$ to the likelihood ratio test statistic, also called ‘deviance function’:
$$
D(\alpha, v)=2\left{\log L_{p}(\hat{\alpha}, \hat{v})-\log L_{p}(\alpha, v)\right}
$$
where $\log L_{p}(\hat{\alpha}, \hat{v})$ is the overall maximum value of the log-likelihood, equivalent to $\log L(\hat{\theta})$. The concept of deviance applies equally to the penalized log-likelihood.
The plots in Fig. 2 displays, in the form of contour level plots, the behaviour of $D(\alpha, v)$ for two artificially generated samples, with $v$ expressed on the logarithmic scale for more convenient readability. Specifically, the top plots refer to a sample of size $n=50$ drawn from the $\operatorname{ST}(0,1,1,2)$; the left plot, refers to the regular log-likelihood, while the right plot refers to the penalized log-likelihood. The plots include marks for points of special interest, as follows:
$\Delta$ the true parameter point;
o the point having maximal (penalized) log-likelihood on a $51 \times 51$ grid of points spanning the plotted area;

the MLE or MPLE point selected by method M0;
the preliminary estimate to be introduced in Sect. 3.2, later denoted M1;
$\times$ the MLE or MPLE point selected by method M2 presented later in the text.

统计代写|生物统计代写biostatistics代考|Preliminary Remarks and the Basic Scheme

We have seen in Sect. 2 the ST log-likelihood function can be problematic; it is then advisable to select carefully the starting point for the MLE search. While contrasting the risk of landing on a local maximum, a connected aspect of interest is to reduce the overall computing time. Here are some preliminary considerations about the stated target.

Since these initial estimates will be refined by a subsequent step of log-likelihood maximization, there is no point in aiming at a very sophisticate method. In addition, we want to keep the involved computing header as light as possible. Therefore, we want a method which is simple and quick to compute; at the same time, it should be reasonably reliable, hopefully avoiding nonsensical outcomes.

Another consideration is that we cannot work with the methods of moments, or some variant of it, as this would impose a condition $v>4$, bearing in mind the constraints recalled in Sect. 1.2. Since some of the most interesting applications of ST-based models deal with very heavy tails, hence with low degrees of freedom, the condition $v>4$ would be unacceptable in many important applications. The implication is that we have to work with quantiles and derived quantities.

To ease exposition, we begin by presenting the logic in the basic case of independent observations from a common univariate distribution $\mathrm{ST}\left(\xi, \omega^{2}, \lambda, v\right)$. The first step is to select suitable quantile-based measures of location, scale,

asymmetry and tail-weight. The following list presents a set of reasonable choices; these measures can be equally referred to a probability distribution or to a sample, depending on the interpretation of the terms quantile, quartile and alike.

Location The median is the obvious choice here; denote it by $q_{2}$, since it coincides with the second quartile.

Scale A commonly used measure of scale is the semi-interquartile difference, also called quartile deviation, that is
$$
d_{q}=\frac{1}{2}\left(q_{3}-q_{1}\right)
$$
where $q_{j}$ denotes the $j$ th quartile; see for instance Kotz et al. (2006, vol. 10, p. 6743).

Asymmetry A classical non-parametric measure of asymmetry is the so-called Bowley’s measure
$$
G=\frac{\left(q_{3}-q_{2}\right)-\left(q_{2}-q_{1}\right)}{q_{3}-q_{1}}=\frac{q_{3}-2 q_{2}+q_{1}}{2 d_{q}}
$$
see Kotz et al. (2006, vol. 12, p. 7771-3). Since the same quantity, up to an inessential difference, had previously been used by Galton, some authors attribute to him its introduction. We shall refer to $G$ as the Galton-Bowley measure.

Kurtosis A relatively more recent proposal is the Moors measure of kurtosis, presented in Moors (1988),
$$
M=\frac{\left(e_{7}-e_{5}\right)+\left(e_{3}-e_{1}\right)}{e_{6}-e_{2}}
$$
where $e_{j}$ denotes the $j$ th octile, for $j=1, \ldots, 7$. Clearly, $e_{2 j}=q_{j}$ for $j=$ $1,2,3$

统计代写|生物统计代写biostatistics代考|Inversion of Quantile-Based Measures to ST Parameters

For the inversion of the parameter set $Q=\left(q_{2}, d_{q}, G, M\right)$ to $\theta=(\xi, \omega, \lambda, v)$, the first stage considers only the components $(G, M)$ which are to be mapped to $(\lambda, v)$, exploiting the invariance of $G$ and $M$ with respect to location and scale. Hence, at this stage, we can work assuming that $\xi=0$ and $\omega=1$.

Start by computing, for any given pair $(\lambda, v)$, the set of octiles $e_{1}, \ldots, e_{7}$ of $\mathrm{ST}(0,1, \lambda, v)$, and from here the corresponding $(G, M)$ values. Operationally, we have computed the ST quantiles using routine qst of package sn. Only nonnegative values of $\lambda$ need to be considered, because a reversal of the $\lambda$ sign simply reverses the sign of $G$, while $M$ is unaffected, thanks to the mirroring property of the ST quantiles when $\lambda$ is changed to $-\lambda$.

Initially, our numerical exploration of the inversion process examined the contour level plots of $G$ and $M$ as functions of $\lambda$ and $v$, as this appeared to be the more natural approach. Unfortunately, these plots turned out not to be useful, because of the lack of a sufficiently regular pattern of the contour curves. Therefore these plots are not even displayed here.

A more useful display is the one adopted in Fig. 3, where the coordinate axes are now $G$ and $M$. The shaded area, which is the same in both panels, represents the set of feasible $(G, M)$ points for the ST family. In the first plot, each of the black lines indicates the locus of points with constant values of $\delta$, defined by (4), when $v$ spans the positive half-line; the selected $\delta$ values are printed at the top of the shaded area, when feasible without clutter of the labels. The use of $\delta$ instead of $\lambda$ simply yields a better spread of the contour lines with different parameter values, but it is conceptually irrelevant. The second plot of Fig. 3 displays the same admissible region with superimposed a different type of loci, namely those corresponding to specified values of $v$, when $\delta$ spans the $[0,1]$ interval; the selected $v$ values are printed on the left side of the shaded area.

Details of the numerical calculations are as follows. The Galton-Bowley and the Moors measures have been evaluated over a $13 \times 25$ grid of points identified by the selected values
$$
\begin{aligned}
\delta^{}=&(0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,0.95,0.99,1) \ v^{}=&(0.30,0.32,0.35,0.40,0.45,0.50,0.60,0.70,0.80,0.90,1,1.5,2\
&3,4,5,7,10,15,20,30,40,50,100, \infty)
\end{aligned}
$$

生物统计代考

统计代写|生物统计代写biostatistics代考|Numerical Aspects and Some Illustrations

由于在计算方面，我们的工作将基于 Azzalini (2019) 描述的 R 包 sn，因此描述该包的一些关键方面是合适的。存在一个用于模型拟合的综合函数，称为 selm，但在 ST 模型的情况下，实际数值工作由函数 st 执行。mple 和 mst。mple，分别在单变量和多变量情况下。为了数值效率，我们将直接使用这些函数，而不是通过 selm。正如他们的名字所暗示的那样，圣。mple 和 mst。mple 执行 MPLE，但它们也可以用于经典 MLE，只需省略惩罚函数。其余的描述指的是圣。mple，但mst。mple 遵循类似的方案。
在单变量情况下，表示为θ=(X,ω,一个,ν)⊤要 cstimatcd 的参数，或者可能θ=(b⊤,在,一个,在)⊤当为位置参数引入 lincar rercssion mudel 时，在这种情况下b是一个向量p回归系数。表示为日志⁡大号(θ)点的对数似然函数θ. 如果没有提供起始值，则 st.mple 的第一个操作是将线性模型拟合到可用的解释变量；这减少到常数协变量值 1 如果p=1. 对于这种线性拟合的残差，计算最多四阶的样本累积量，因此包括样本方差。从这些倒置

值到θ可能或不可能，取决于第三个和第四个样本累积量是否落在 ST 系列的可行区域内。如果反演成功，则得到参数的初始值；如果没有，最后两个组件θ设置在(一个,在)=(0,10)，保留线性拟合中的其他分量。从这一点开始，使用一般数值优化程序搜索 MLE 或 MPLE。执行此步骤的默认程序是R函数 nlminb，除了对数似然函数外，还提供分数函数。我们将把这个目前的标准程序统称为“方法 M0”。

在我们所有的数值工作中，方法 M0 使用 st。mple 和涉及的函数 nlminb，所有调整参数都保持在默认值。唯一激活的选项是在 MPLE 和 MLE 之间切换，甚至这仅适用于本节的工作。稍后，我们将始终使用带有惩罚函数 Openalty 的 MPLE，它实现了 Azzalini 和 Arellano-Valle (2013) 中提出的方法。

我们从一些模拟数据集生成的对数似然的插图开始我们的数值工作，基本上以图形形式。目的是提供对数似然的可能行为以及它为 MLE 搜索和其他推理过程带来的后续问题的直接感知，尽管不可避免地受到限制。鉴于这一目标，我们专注于以某种方式不寻常的案件，而不是“普通案件”。

我们采用的图形显示类型是基于轮廓对数似然函数(一个,在), 表示日志⁡大号p(一个,在). 这是获得的，对于任何给定的(一个,在)，通过最大化日志⁡大号(θ)关于其余参数。为了简化可读性，我们将日志⁡大号p(一个,在)似然比检验统计量，也称为“偏差函数”：

D(\alpha, v)=2\left{\log L_{p}(\hat{\alpha}, \hat{v})-\log L_{p}(\alpha, v)\right}D(\alpha, v)=2\left{\log L_{p}(\hat{\alpha}, \hat{v})-\log L_{p}(\alpha, v)\right}
在哪里日志⁡大号p(一个^,在^)是对数似然的整体最大值，相当于日志⁡大号(θ^). 偏差的概念同样适用于惩罚对数似然。
图 2 中的图以等高线水平图的形式显示了D(一个,在)对于两个人工生成的样本，在以对数刻度表示，以便于阅读。具体来说，上面的图是指一个大小的样本n=50取自英石⁡(0,1,1,2); 左图是指常规对数似然，而右图是指惩罚对数似然。这些图包括特殊兴趣点的标记，如下所示：
Δ真正的参数点；
o 在 a 上具有最大（惩罚）对数似然的点51×51跨越绘图区域的点网格；

方法 M0 选择的 MLE 或 MPLE 点；
将在 Sect 中介绍的初步估计。3.2，后面记为M1；
×文中稍后介绍的方法 M2 选择的 MLE 或 MPLE 点。

统计代写|生物统计代写biostatistics代考|Preliminary Remarks and the Basic Scheme

我们在教派中见过。2 ST 对数似然函数可能有问题；然后建议仔细选择 MLE 搜索的起点。在对比着陆到局部最大值的风险时，感兴趣的一个相关方面是减少整体计算时间。以下是关于既定目标的一些初步考虑。

由于这些初始估计将通过对数似然最大化的后续步骤进行细化，因此以非常复杂的方法为目标是没有意义的。此外，我们希望使所涉及的计算头尽可能轻。因此，我们需要一种简单快速计算的方法；同时，它应该是相当可靠的，希望能避免无意义的结果。

另一个考虑是，我们不能使用矩量方法或它的一些变体，因为这会强加一个条件在>4，牢记 Sect 中回忆的约束。1.2. 由于基于 ST 的模型的一些最有趣的应用处理非常重的尾部，因此具有低自由度，条件在>4在许多重要应用中是不可接受的。这意味着我们必须使用分位数和派生数量。

为了便于说明，我们首先介绍来自共同单变量分布的独立观察的基本情况下的逻辑小号吨(X,ω2,λ,在). 第一步是选择合适的基于分位数的位置、规模、

不对称和尾重。下面列出了一组合理的选择；根据对分位数、四分位数等术语的解释，这些度量可以同样称为概率分布或样本。

位置中位数是这里的明显选择；表示为q2，因为它与第二个四分位数一致。

尺度常用的尺度度量是半四分位差，也称为四分位差，即

dq=12(q3−q1)
在哪里qj表示j第四分位数；例如，参见 Kotz 等人。（2006 年，第 10 卷，第 6743 页）。

不对称不对称的经典非参数度量是所谓的鲍利度量

G=(q3−q2)−(q2−q1)q3−q1=q3−2q2+q12dq
参见 Kotz 等人。（2006 年，第 12 卷，第 7771-3 页）。由于高尔顿之前使用了相同的数量，但存在无关紧要的差异，因此一些作者将其归因于他的介绍。我们将参考G作为 Galton-Bowley 度量。

峰度一个相对较新的建议是 Moors 峰度测量，在 Moors (1988) 中提出，

米=(和7−和5)+(和3−和1)和6−和2
在哪里和j表示j八分位数，对于j=1,…,7. 清楚地，和2j=qj为了j= 1,2,3

统计代写|生物统计代写biostatistics代考|Inversion of Quantile-Based Measures to ST Parameters

对于参数集的反演问=(q2,dq,G,米)至θ=(X,ω,λ,在)，第一阶段只考虑组件(G,米)要映射到的(λ,在)，利用不变性G和米关于位置和规模。因此，在这个阶段，我们可以假设X=0和ω=1.

从计算开始，对于任何给定的对(λ,在), 八分位数的集合和1,…,和7的小号吨(0,1,λ,在)，从这里对应的(G,米)价值观。在操作上，我们使用包 sn 的例程 qst 计算了 ST 分位数。只有非负值λ需要考虑，因为逆转λ符号只是反转符号G，尽管米不受影响，这要归功于 ST 分位数的镜像属性，当λ改为−λ.

最初，我们对反演过程的数值探索检查了等值线水平图G和米作为函数λ和在，因为这似乎是更自然的方法。不幸的是，这些图没有用，因为轮廓曲线缺乏足够规则的图案。因此，这些图甚至没有在这里显示。

更有用的显示是图 3 中采用的显示，其中坐标轴现在是G和米. 两个面板中相同的阴影区域表示可行的集合(G,米)ST家族的积分。在第一个图中，每条黑线表示具有常数值的点的轨迹d，由 (4) 定义，当在跨越正半线；被选中的d值打印在阴影区域的顶部，如果可行，标签不会混乱。指某东西的用途d代替λ简单地产生具有不同参数值的等高线的更好分布，但它在概念上无关紧要。图 3 的第二个图显示了相同的允许区域，其中叠加了不同类型的基因座，即对应于指定值的基因座在，什么时候d跨越[0,1]间隔; 被选中的在值打印在阴影区域的左侧。

数值计算的细节如下。Galton-Bowley 和 Moors 措施已经过评估13×25由所选值标识的点网格

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|BIOL 220

Posted on 2022年6月28日2022年6月28日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|Flexible Distributions: The Skew-t Case

In the context of distribution theory, a central theme is the study of flexible parametric families of probability distributions, that is, families allowing substantial variation of their behaviour when the parameters span their admissible range.

For brevity, we shall refer to this domain with the phrase ‘flexible distributions’. The archetypal construction of this logic is represented by the Pearson system of curves for univariate continuous variables. In this formulation, the density function is regulated by four parameters, allowing wide variation of the measures of skewness and kurtosis, hence providing much more flexibility than in the basic case represented by the normal distribution, where only location and scale can be adjusted.

Since Pearson times, flexible distributions have remained a persistent theme of interest in the literature, with a particularly intense activity in recent years. A prominen feature of newer developments is the increased sonsideration for multivariate distributions, reflecting the current availability in applied work of larger datasets, both in sample size and in dimensionality. In the multivariate setting, the various formulations often feature four blocks of parameters to regulate location, scale, skewness and kurtosis.

While providing powerful tools for data fitting, flexible distributions also pose some challenges when we enter the concrete estimation stage. We shall be working with maximum likelihood estimation (MLE) or variants of it, but qualitatively similar issues exist for other criteria. Explicit expressions of the estimates are out of the question; some numerical optimization procedure is always involved and this process is not so trivial because of the larger number of parameters involved, as compared with fitting simpler parametric models, such as a Gamma or a Beta distribution. Furthermore, in some circumstances, the very flexibility of these parametric families can lead to difficulties: if the data pattern does not aim steadily towards a certain point of the parameter space, there could be two or more such points which constitute comparably valid candidates in terms of log-likelihood or some other estimation criterion. Clearly, these problems are more challenging with small sample size, later denoted $n$, since the log-likelihood function (possibly tuned by a prior distribution) is relatively more flat, but numerical experience has shown that they can persist even for fairly large $n$, in certain cases.

统计代写|生物统计代写biostatistics代考|The Skew-t Distribution: Basic Facts

Before entering our actual development, we recall some basic facts about the ST parametric family of continuous distributions. In its simplest description, it is obtained as a perturbation of the classical Student’s $t$ distribution. For a more specific description, start from the univariate setting, where the components of the family are identified by four parameters. Of these four parameters, the one denoted $\xi$ in the following regulates the location of the distribution; scale is regulated by the positive parameter $\omega$; shape (representing departure from symmetry) is regulated by $\lambda$; tail-weight is regulated by $v$ (with $v>0$ ), denoted ‘degrees of freedom’ like for a classical $t$ distribution.

It is convenient to introduce the distribution in the ‘standard case’, that is, with location $\xi=0$ and scale $\omega=1$. In this case, the density function is
$$
t(z ; \lambda, v)=2 t(z ; v) T\left(\lambda z \sqrt{\frac{v+1}{v+z^{2}}} ; v+1\right), \quad z \in \mathbb{R}
$$

where
$$
t(z ; v)=\frac{\Gamma\left(\frac{1}{2}(v+1)\right)}{\sqrt{\pi v} \Gamma\left(\frac{1}{2} v\right)}\left(1+\frac{z^{2}}{v}\right)^{-(v+1) / 2}, \quad z \in \mathbb{R}
$$
is the density function of the classical Student’s $t$ on $v$ degrees of freedom and $T(\cdot ; v)$ denotes its distribution function; note however that in (1) this is evaluated with $v+1$ degrees of freedom. Also, note that the symbol $t$ is used for both densities in (1) and (2), which are distinguished by the presence of either one or two parameters.

If $Z$ is a random variable with density function (1), the location and scale transform $Y=\xi+\omega Z$ has density function
$$
t_{Y}(x ; \theta)=\omega^{-1} t(z ; \lambda, v), \quad z=\omega^{-1}(x-\xi),
$$
where $\theta=(\xi, \omega, \lambda, v)$. In this case, we write $Y \sim \operatorname{ST}\left(\xi, \omega^{2}, \lambda, v\right)$, where $\omega$ is squared for similarity with the usual notation for normal distributions.

When $\lambda=0$, we recover the scale-and-location family generated by the $t$ distribution (2). When $v \rightarrow \infty$, we obtain the skew-normal (SN) distribution with parameters $(\xi, \omega, \lambda)$, which is described for instance by Azzalini and Capitanio (2014, Chap. 2). When $\lambda=0$ and $v \rightarrow \infty$, (3) converges to the $\mathrm{N}\left(\xi, \omega^{2}\right)$ distribution.

Some instances of density (1) are displayed in the left panel of Fig. 1. If $\lambda$ was replaced by $-\lambda$, the densities would be reflected on the opposite side of the vertical axis, since $-Y \sim \operatorname{ST}\left(-\xi, \omega^{2},-\lambda, \nu\right)$.

统计代写|生物统计代写biostatistics代考|Basic General Aspects

The high flexibility of the ST distribution makes it particularly appealing in a wide range of data fitting problems, more than its companion, the SN distribution. Reliable techniques for implementing connected MLE or other estimation methods are therefore crucial.

From the inference viewpoint, another advantage of the ST over the related SN distribution is the lack of a stationary point at $\lambda=0$ (or $\alpha=0$ in the multivariate case), and the implied singularity of the information matrix. This stationary point of the SN is systematic: it occurs for all samples, no matter what $n$ is. This peculiar aspect has been emphasized more than necessary in the literature, considering that it pertains to a single although important value of the parameter. Anyway, no such problem exists under the ST assumption. The lack of a stationary point at the origin was first observed empirically and welcomed as ‘a pleasant surprise’ by Azzalini and Capitanio (2003), but no theoretical explanation was given. Additional numerical evidence in this direction has been provided by Azzalini and Genton (2008). The theoretical explanation of why the SN and the ST likelihood functions behave differently was finally established by Hallin and Ley (2012).

Another peculiar aspect of the SN likelihood function is the possibility that the maximum of the likelihood function occurs at $\lambda=\pm \infty$, or at $|\alpha| \rightarrow \infty$ in the multivariate case. Note that this happens without divergence of the likelihood function, but only with divergence of the parameter achieving the maximum. In this respect the SN and the ST model are similar: both of them can lead to this pattern.
Differently from the stationarity point at the origin, the phenomenon of divergent estimates is transient: it occurs mostly with small $n$, and the probability of its occurrence decreases very rapidly when $n$ increases. However, when it occurs for the $n$ available data, we must handle it. There are different views among statisticians on whether such divergent values must be retained as valid estimates or they must be rejected as unacceptable. We embrace the latter view, for the reasons put forward by Azzalini and Arellano-Valle (2013), and adopt the maximum penalized likelihood estimate (MPLE) proposed there to prevent the problem. While the motivation for MPLE is primarily for small to moderate $n$, we use it throughout for consistency.
There is an additional peculiar feature of the ST log-likelihood function, which however we mention only for completeness, rather than for its real relevance. In cases when $v$ is allowed to span the whole positive half-line, poles of the likelihood function must exist near $v=0$, similarly to the case of a Student’s $t$ with unspecified degrees of freedom. This problem has been explored numerically by Azzalini and Capitanio (2003, pp. 384-385), and the indication was that these poles must exist at very small values of $v$, such as $\hat{v}=0.06$ in one specific instance.

This phenomenon is qualitatively similar to the problem of poles of the likelihood function for a finite mixture of continuous distributions. Even in the simple case of univariate normal components, there always exist $n$ poles on the boundary of the parameter space if the standard deviations of the components are unrestricted; see for instance Day (1969, Section 7). The problem is conceptually interesting, in both settings, but in practice it is easily dealt with in various ways. In the ST setting, the simplest solution is to impose a constraint $v>v_{0}>0$ where $v_{0}$ is some very small value, such as $v_{0}=0.1$ or $0.2$. Even if fitted to data, a $t$ or ST density with $v<0.1$ would be an object hard to use in practice.

生物统计代考

统计代写|生物统计代写biostatistics代考|Flexible Distributions: The Skew-t Case

在分布理论的背景下，一个中心主题是研究概率分布的灵活参数族，即当参数跨越其允许范围时，允许其行为发生实质性变化的族。

为简洁起见，我们将使用短语“灵活分布”来指代这个领域。该逻辑的原型构造由单变量连续变量的 Pearson 曲线系统表示。在这个公式中，密度函数由四个参数调节，允许偏度和峰度测量的广泛变化，因此提供比正态分布表示的基本情况更大的灵活性，其中只能调整位置和规模。

自 Pearson 时代以来，灵活分布一直是文献中持续关注的主题，近年来活动尤为激烈。新发展的一个显着特征是对多元分布的更多考虑，这反映了当前在更大数据集的应用工作中的可用性，无论是在样本大小还是维度上。在多变量设置中，各种公式通常具有四个参数块来调节位置、规模、偏度和峰度。

在为数据拟合提供强大工具的同时，当我们进入具体的估计阶段时，灵活的分布也带来了一些挑战。我们将使用最大似然估计 (MLE) 或其变体，但其他标准存在质量上类似的问题。估计的明确表达是不可能的；与拟合更简单的参数模型（例如 Gamma 或 Beta 分布）相比，总是涉及一些数值优化过程，并且由于涉及的参数数量较多，因此该过程并不是那么简单。此外，在某些情况下，这些参数族的灵活性可能会导致困难：如果数据模式没有稳定地指向参数空间的某个点，在对数似然或一些其他估计标准方面，可能有两个或更多这样的点构成相当有效的候选者。显然，这些问题在样本量较小的情况下更具挑战性，稍后表示n，因为对数似然函数（可能由先验分布调整）相对更平坦，但数值经验表明它们可以持续相当大n, 在某些情况下。

统计代写|生物统计代写biostatistics代考|The Skew-t Distribution: Basic Facts

在进入我们的实际开发之前，我们回顾一下关于连续分布的 ST 参数族的一些基本事实。在最简单的描述中，它是作为经典学生的扰动获得的吨分配。对于更具体的描述，从单变量设置开始，其中族的组件由四个参数标识。在这四个参数中，一个表示X在下文中规定了分配的位置；规模由正参数调节ω; 形状（代表背离对称）由λ; 尾重由在（和在>0)，表示“自由度”，就像经典的吨分配。

在“标准情况”中引入分布很方便，即带有位置X=0和规模ω=1. 在这种情况下，密度函数是

吨(和;λ,在)=2吨(和;在)吨(λ和在+1在+和2;在+1),和∈R

在哪里

吨(和;在)=Γ(12(在+1))圆周率在Γ(12在)(1+和2在)−(在+1)/2,和∈R
是经典学生的密度函数吨上在自由度和吨(⋅;在)表示其分布函数；但是请注意，在（1）中，这是用在+1自由程度。另外，请注意符号吨用于 (1) 和 (2) 中的两个密度，它们的区别在于存在一个或两个参数。

如果从是具有密度函数 (1) 的随机变量，位置和尺度变换是=X+ω从有密度函数

吨是(X;θ)=ω−1吨(和;λ,在),和=ω−1(X−X),
在哪里θ=(X,ω,λ,在). 在这种情况下，我们写是∼英石⁡(X,ω2,λ,在)，在哪里ω为与正态分布的通常表示法相似的平方。

什么时候λ=0，我们恢复由吨分布 (2)。什么时候在→∞，我们得到带有参数的偏正态（SN）分布(X,ω,λ)，例如由 Azzalini 和 Capitanio（2014 年，第 2 章）描述。什么时候λ=0和在→∞, (3) 收敛到ñ(X,ω2)分配。

密度 (1) 的一些实例显示在图 1 的左侧面板中。如果λ被替换为−λ，密度将反映在垂直轴的另一侧，因为−是∼英石⁡(−X,ω2,−λ,ν).

统计代写|生物统计代写biostatistics代考|Basic General Aspects

ST 分布的高度灵活性使其在广泛的数据拟合问题中特别有吸引力，超过了它的同伴 SN 分布。因此，实现互联 MLE 或其他估计方法的可靠技术至关重要。

从推理的角度来看，ST 相对于相关 SN 分布的另一个优势是在λ=0（或者一个=0在多变量情况下），以及信息矩阵的隐含奇异性。SN 的这个驻点是系统性的：它出现在所有样本中，无论如何n是。考虑到它与参数的单个但重要的值有关，在文献中已经过分强调了这一特殊方面。无论如何，在ST假设下不存在这样的问题。Azzalini 和 Capitanio（2003 年）首先凭经验观察到原点缺乏静止点，并称其为“惊喜”，但没有给出理论解释。Azzalini 和 Genton (2008) 提供了这方面的额外数字证据。Hallin 和 Ley (2012) 最终建立了关于 SN 和 ST 似然函数为何表现不同的理论解释。

SN 似然函数的另一个特殊方面是似然函数的最大值出现在λ=±∞，或|一个|→∞在多变量情况下。请注意，这种情况在似然函数没有发散的情况下发生，但只有在参数的发散达到最大值的情况下才会发生。在这方面，SN 和 ST 模型是相似的：它们都可以导致这种模式。
与原点的平稳点不同，估计发散现象是短暂的：它主要发生在小n，并且它发生的概率在当n增加。然而，当它发生在n可用的数据，我们必须处理它。对于是否必须将这些不同的值保留为有效估计值还是必须将其视为不可接受的值而拒绝，统计学家之间存在不同的看法。由于 Azzalini 和 Arellano-Valle (2013) 提出的原因，我们接受后一种观点，并采用那里提出的最大惩罚似然估计 (MPLE) 来防止该问题。虽然 MPLE 的动机主要是针对中小型n，我们始终使用它以保持一致性。
ST 对数似然函数还有一个额外的特殊功能，但是我们仅出于完整性而不是其真正相关性而提及它。在某些情况下在允许跨越整个正半线，似然函数的极点必须存在于附近在=0，类似于学生的情况吨具有未指定的自由度。Azzalini 和 Capitanio (2003, pp. 384-385) 对这个问题进行了数值研究，表明这些极点必须以非常小的值存在在，如在^=0.06在一个特定的情况下。

这种现象在性质上类似于连续分布的有限混合的似然函数极点问题。即使在单变量正态分量的简单情况下，也总是存在n如果分量的标准差不受限制，则参数空间边界上的极点；参见例如 Day (1969, Section 7)。在这两种情况下，这个问题在概念上都很有趣，但在实践中，它很容易以各种方式处理。在 ST 设置中，最简单的解决方案是施加约束在>在0>0在哪里在0是一些非常小的值，比如在0=0.1或者0.2. 即使适合数据，a吨或 ST 密度与在<0.1将是一个难以在实践中使用的对象。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考| DETERMINING THE SAMPLE SIZE

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考| DETERMINING THE SAMPLE SIZE

统计代写|生物统计代写biostatistics代考|The Sample Size for Simple and Systematic Random Samples

In a simple random sample or a systematic random sample, the sample size required to produce a prespecified bound on the error of estimation for estimating the mean is based on the number of units in the population $(N)$, and the approximate variance of the population $\sigma^{2}$. Moreover, given the values of $N$ and $\sigma^{2}$, the sample size required for estimating a mean $\mu$ with bound on the error of estimation $B$ with a simple or systematic random sample is
$$
n=\frac{N \sigma^{2}}{(N-1) D+\sigma^{2}}
$$
where $D=\frac{B^{2}}{4}$. Note that this formula will not generally return a whole number for the sample size $n$; when the formula does not return a whole number for the sample size, the sample size should be taken to be the next largest whole number.
Example 3.11
Suppose a simple random sample is going to be taken from a population of $N=5000$ units with a variance of $\sigma^{2}=50$. If the bound on the error of estimation of the mean is supposed to be $B=1.5$, then the sample size required for the simple random sample selected from this population is
$$
n=\frac{5000(50)}{4999\left(\frac{1.5^{2}}{4}\right)+50}=87.35
$$
Since $87.35$ units cannot be sampled, the sample size that should be used is $n=88$. Also, $n=$ 88 would be the sample size required for a systematic random sample from this population when the desired bound on the error of estimation for estimating the mean is $B=1.5$. In this case, the systematic random sample would be a 1 in 56 systematic random sample since $\frac{5000}{88} \approx 56$.

In many research projects, the values of $N$ or $\sigma^{2}$ are often unknown. When either $N$ or $\sigma^{2}$ is unknown, the formula for determining the sample size to produce a bound on the error of estimation for a simple random sample can still be used as long as the approximate values of $N$ and $\sigma^{2}$ are available. In this case, the resulting sample size will produce a bound on the error of estimation that is close to $B$ provided the approximate values of $N$ and $\sigma^{2}$ are reasonably accurate.

The proportion of the units in the population that are sampled is $n / N$, which is called the sampling proportion. When a rough guess of the size of the population cannot be reasonably made, but it is clear that the sampling proportion will be less than $5 \%$, then an alternative formula for determining the sample size is needed. In this case, the sample size required for a simple random sample or a systematic random sample having bound on the error of estimation $B$ for estimating the mean is approximately
$$
n=\frac{4 \sigma^{2}}{B^{2}}
$$

统计代写|生物统计代写biostatistics代考|The Sample Size for a Stratified Random Sample

Recall that a stratified random sample is simply a collection of simple random samples selected from the subpopulations in the target population. In a stratified random sample, there are two sample size considerations, namely, the overall sample size $n$ and the allocation of $n$ units over the strata. When there are $k$ strata, the strata sample sizes will be denoted by $n_{1}, n_{2}, n_{3}, \ldots, n_{k}$, where the number to be sampled in strata 1 is $n_{1}$, the number to be sampled in strata 2 is $n_{2}$, and so on.

There are several different ways of determining the overall sample size and its allocation in a stratified random sample. In particular, proportional allocation and optimal allocation are two commonly used allocation plans. Throughout the discussion of these two allocation plans, it will be assumed that the target population has $k$ strata, $N$ units, and $N_{j}$ is the number of units in the $j$ th stratum.

The sample size used in a stratified random sample and the most efficient allocation of the sample will depend on several factors including the variability within each of the strata, the proportion of the target population in each of the strata, and the costs associated with sampling the units from the strata. Let $\sigma_{i}$ be the standard deviation of the $i$ th stratum, $W_{i}=N_{i} / N$ the proportion of the target population in the $i$ th stratum, $C_{0}$ the initial cost of sampling, $C_{i}$ the cost of obtaining an observation from the $i$ th stratum, and $C$ is the total cost of sampling. Then, the cost of sampling with a stratified random sample is
$$
C=C_{0}+C_{1} n_{1}+C_{2} n_{2}+\cdots+C_{k} n_{k}
$$
The process of determining the sample size for a stratified random sample requires that the allocation of the sample be determined first. The allocation of the sample size $n$ over the $k$ strata is based on the sampling proportions that are denoted by $w_{1}, w_{2}, \ldots w_{k}$. Once the sampling proportions and the overall sample size $n$ have been determined, the $i$ th stratum sample size is $n_{i}=n \times w_{i}$.

The simplest allocation plan for a stratified random sample is proportional allocation that takes the sampling proportions to be proportional to the strata sizes. Thus, in proportional allocation, the sampling proportion for the $i$ th stratum is equal to the proportion of the population in the ith stratum. That is, the sampling proportion for the $i$ th stratum is
$$
w_{i}=\frac{N_{i}}{N}
$$
The overall sample size for a stratified random sample based on proportional allocation that will have bound on error of estimation for estimating the mean equal to $B$ is
$$
n=\frac{N_{1} \sigma_{1}^{2}+N_{2} \sigma_{2}^{2}+\cdots+N_{k} \sigma_{k}^{2}}{N\left[\frac{B^{2}}{4}\right]+\frac{1}{N}\left(N_{1} \sigma_{1}^{2}+N_{2} \sigma_{2}^{2}+\cdots+N_{k} \sigma_{k}^{2}\right)}
$$
The sample size for the simple random sample that will be selected from the $i$ th stratum according to proportional allocation is
$$
n \times w_{i}=n \times \frac{N_{i}}{N}
$$

统计代写|生物统计代写biostatistics代考|Bar and Pie Charts

In the case of qualitative or discrete data, the graphical statistics that are most often used to summarize the data in the observed sample are the bar chart and the pie chart since the

important parameters of the distribution of a qualitative variable are population proportions. Thus, for a qualitative variable the sample proportions are the values that will be displayed in a bar chart or a pie chart.

In Chapter 2, the distribution of a qualitative variable was often presented in a bar chart in which the height of a bar represented the proportion or the percentage of the population having each quality the variable takes on. With an observed sample, bar charts can be used to represent the sample proportions or percentages for each of the qualities the variable takes on and can be used to make statistical inferences about the population distribution of the variable.

There are many types of bar charts including simple bar charts, stacked bar charts, and comparative side-by-side bar charts. An example of a simple bar chart for the weight classification for babies, which takes on the values normal and low, in the Birth Weight data set is shown in Figure 4.1.

Note that a bar chart represents the category percentages or proportions with bars of height equal to the percentage or proportion of sample observations falling in a particular category. The widths of the bars should be equal and chosen so that an appealing chart is produced. Bar charts may be drawn with either horizontal or vertical bars, and the bars in a bar chart may or may not be separated by a gap. An example of a bar chart with horizontal bars is given in Figure $4.2$ for the weight classification of babies in the Birth Weight data set.
In creating a bar chart it is important that

the proportions or percentages in each bar can be easily determined to make the bar chart easier to read and interpret.
the total percentage represented in the bar chart should be 100 since a distribution contains $100 \%$ of the population units.
the qualities associated with an ordinal variable are listed in the proper relative order! With a nominal variable the order of the categories is not important.
the bar chart has the axes of the bar chart clearly labeled so that it is clear whether the bars represent a percentage or a proportion.
the bar chart has either a caption or a title that clearly describes the nature of the bar chart.

生物统计代考

统计代写|生物统计代写biostatistics代考|The Sample Size for Simple and Systematic Random Samples

在简单随机样本或系统随机样本中，为估计均值而对估计误差产生预先指定的界限所需的样本量基于总体中的单位数(ñ)，以及总体的近似方差σ2. 此外，鉴于ñ和σ2, 估计平均值所需的样本量μ估计误差有界乙一个简单或系统的随机样本是

n=ñσ2(ñ−1)D+σ2
在哪里D=乙24. 请注意，此公式通常不会返回样本量的整数n; 当公式没有返回样本量的整数时，应将样本量取为下一个最大的整数。
例 3.11
假设一个简单的随机样本将从人口中抽取ñ=5000方差为的单位σ2=50. 如果平均值估计误差的界限应该是乙=1.5，则从该总体中选择的简单随机样本所需的样本量为

n=5000(50)4999(1.524)+50=87.35
自从87.35单位不能被抽样，应该使用的样本量是n=88. 还，n=当估计平均值的估计误差的期望界限为乙=1.5. 在这种情况下，系统随机样本将是 56 个系统随机样本中的 1 个，因为500088≈56.

在许多研究项目中，ñ或者σ2往往是未知的。当ñ或者σ2是未知的，确定样本大小以产生一个简单随机样本的估计误差界限的公式仍然可以使用，只要近似值ñ和σ2可用。在这种情况下，得到的样本量将产生一个接近于估计误差的界限乙提供的近似值ñ和σ2是相当准确的。

被抽样单位在总体中的比例为n/ñ，称为抽样比例。当无法合理地对总体规模做出粗略的猜测，但很明显抽样比例会小于5%，则需要一个用于确定样本量的替代公式。在这种情况下，简单随机样本或系统随机样本所需的样本量限制了估计误差乙估计平均值大约是

n=4σ2乙2

统计代写|生物统计代写biostatistics代考|The Sample Size for a Stratified Random Sample

回想一下，分层随机样本只是从目标人群的亚群中选择的简单随机样本的集合。在分层随机样本中，有两个样本量考虑，即总体样本量n和分配n地层上的单位。当有ķ分层，分层样本大小将表示为n1,n2,n3,…,nķ，其中第 1 层中要采样的数量是n1，第 2 层中要采样的数量为n2，等等。

有几种不同的方法可以确定总体样本量及其在分层随机样本中的分配。尤其是比例分配和最优分配是两种常用的分配方案。在这两个分配计划的讨论中，将假设目标人群有ķ地层，ñ单位，和ñj是单元的数量j第层。

分层随机样本中使用的样本量和样本的最有效分配将取决于几个因素，包括每个层内的可变性、每个层中目标人群的比例以及与抽样相关的成本来自地层的单位。让σ一世是标准差一世第层，在一世=ñ一世/ñ目标人群的比例一世第层，C0抽样的初始成本，C一世获得观察的成本一世th 层，和C是抽样的总成本。那么，分层随机样本的抽样成本为

C=C0+C1n1+C2n2+⋯+Cķnķ
确定分层随机样本的样本量的过程需要首先确定样本的分配。样本量的分配n超过ķ分层基于由表示的抽样比例在1,在2,…在ķ. 一旦抽样比例和总体样本量n已经确定，一世第层样本量为n一世=n×在一世.

分层随机样本的最简单分配计划是比例分配，它使抽样比例与分层大小成比例。因此，在比例分配中，一世第 th 层等于第 i 层中人口的比例。即，抽样比例为一世第层是

在一世=ñ一世ñ
基于比例分配的分层随机样本的总样本量，估计平均值的估计误差为乙是

n=ñ1σ12+ñ2σ22+⋯+ñķσķ2ñ[乙24]+1ñ(ñ1σ12+ñ2σ22+⋯+ñķσķ2)
将从中选择的简单随机样本的样本量一世根据比例分配的第层是

n×在一世=n×ñ一世ñ

统计代写|生物统计代写biostatistics代考|Bar and Pie Charts

在定性或离散数据的情况下，最常用于总结观察样本中数据的图形统计是条形图和饼图，因为

定性变量分布的重要参数是人口比例。因此，对于定性变量，样本比例是将显示在条形图或饼图中的值。

在第 2 章中，定性变量的分布通常以条形图的形式呈现，其中条形的高度表示具有该变量所具有的每种质量的总体的比例或百分比。对于观察到的样本，条形图可用于表示变量所具有的每种质量的样本比例或百分比，并可用于对变量的总体分布进行统计推断。

有许多类型的条形图，包括简单条形图、堆叠条形图和比较并排条形图。图 4.1 显示了婴儿体重分类的简单条形图示例，它在出生体重数据集中采用正常值和低值。

请注意，条形图表示类别百分比或比例，高度条的高度等于样本观测值落入特定类别的百分比或比例。条形的宽度应相等并进行选择，以便生成吸引人的图表。条形图可以用水平或垂直条形绘制，条形图中的条形可能会或可能不会被间隙分隔。图 1 给出了一个带有水平条的条形图示例4.2用于出生体重数据集中婴儿的体重分类。
在创建条形图时，重要的是

可以轻松确定每个条形中的比例或百分比，以使条形图更易于阅读和解释。
条形图中表示的总百分比应为 100，因为分布包含100%人口单位。
与序数变量相关的质量以正确的相对顺序列出！对于名义变量，类别的顺序并不重要。
条形图清楚地标记了条形图的轴，以便清楚条形是代表百分比还是比例。
条形图具有清楚地描述条形图性质的标题或标题。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考| RANDOM SAMPLING

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考| RANDOM SAMPLING

统计代写|生物统计代写biostatistics代考|OBTAINING REPRESENTATIVE DATA

The purpose of sampling is to get a sufficient amount of data that is representative of target population so that statistical inferences can be made about the distribution and the parameters of the target population. Because a sample is only a subset of the units in the target population, it is generally impossible to guarantee that the sample data are representative of the target population; however, with a well-designed sampling plan, it will be unlikely to select a sample that is not representative of the target population. To ensure the likelihood that the sample data will be representative of the target population, the following components of the sampling process must be considered:

Target Population The target population must be well defined, accessible, and the researcher should have a good understanding of the structure of the population. In particular, the researcher should be able to identify the units of the population, the approximate number of units in the population, subpopulations, the approximate shape of the distributions of the variables being studied, and the relevant parameters that need to be estimated.
Sampling Units The Sampling units are the units of the population that will be sampled. A sampling unit may or may not be a unit of the population. In fact, in some sampling plans, the sampling unit is a collection of population units. The sampling unit is also the smallest unit in the target population that can be selected.
Sampling Element A sampling element is an object on which measurements will be made. A sampling element may or may not be a sampling unit. When the sampling unit consists of several population units, it is called a cluster of units. If each

population unit in a cluster will be measured, then the sampling elements are the population units within the sampled clusters. In this case, the sampling element is a subunit of the sampling unit.

Sampling Frame The sampling frame is the list of sampling units that are available for sampling. The sampling frame should be nearly equal to the target population. When the sampling frame is significantly different from the target population, it makes it less unlikely that a sample representative of the target population will be obtained, even with a well-designed sampling plan. Sampling frames that fail to include all of the units of the target population are said to undercover the target population and may lead to biased samples.
Sample Size The sample size is the number of sampling units that will be selected. The sample size will be denoted by $n$ and must be sufficiently large to ensure the reliability of the statistical analysis. The variability in the target population plays a key role in determining the sample size necessary for the desired level of reliability associated with a statistical analysis.

统计代写|生物统计代写biostatistics代考|Probability Samples

The statistical theory that provides the foundation for the estimation or testing of research hypotheses about the parameters of a population is based on the sampling structure known as probability sampling. A probability sample is a sample that is selected in a random fashion according to some probability model. In particular, a probability sample is a sample chosen so that each of the possible samples is known in advance and the probability of drawing each sampling unit is known. Random samples are samples that arise through a sampling plan based on probability sampling.

Probability sampling allows flexibility in the sampling plan and can be designed specifically for the target population being studied. That is, a probability sampling plan allows a sample to be designed so that it will be unlikely to produce a sample that is not representative of the target population. Furthermore, probability samples allow for confidence statements and hypothesis tests to be made from the observed sample with a high degree of reliability.

Samples of convenience are samples that are not based on probability samples and are also referred to as nonprobability samples. The statistical theory that justifies the use of confidence statements and tests of hypotheses does not apply to nonprobability samples; therefore, confidence statements and test of the research hypotheses based on nonprobability samples are erroneous applications of statistics and should not be trusted.
In a random sample, the chance that a particular unit of the population will be selected is known prior to sampling, and the units available for sampling are selected at random according to these probabilities. The procedure for drawing a random sample is outlined below.

统计代写|生物统计代写biostatistics代考|Simple Random Sampling

The first sampling plan that will be discussed is the simple random sample. A simple random sample of size $n$ is a sample consisting of $n$ sampling units selected in a fashion that every possible sample of $n$ units has the same chance of being selected. In a simple random sample, every possible sample has the same chance of being selected, and moreover, each sampling unit has the same chance of being drawn in a sample. Simple random sampling is a reasonable sampling plan for sampling homogeneous or heterogeneous populations that do not have distinct subpopulations that are of interest to the researcher.
Example 3.3
Simple random sampling might be a reasonable sampling plan in the following scenarios:
a. A pharmaceutical company is checking the quality control issues of the tablet form of a new drug. Here, the company might take a random sample of tablets from a large pool of available drug tablets it has recently manufactured.
b. The Federal Food and Drug Administration (FDA) may take a simple random sample of a particular food product to check the validity of the information on the nutrition label.
c. A state might wish to take a simple random sample of medical doctors to review whether or not the state’s continuing education requirements are being satisfied.
d. A federal or state environment agency may wish to take a simple random sample of homes in a mining town to investigate the general health of the town’s inhabitants and contamination problems in the homes resulting from the mining operation.

The number of possible simple random samples of size $n$ selected from a sampling frame listing of $N$ sampling units is
$$
\left(\begin{array}{l}
N \
n
\end{array}\right)=\frac{N !}{n !(N-n) !}
$$
The probability that any one of the possible simple random samples of $n$ units selected from a sampling frame of $N$ units is
$$
\frac{1}{\frac{N !}{n !(N-n) !}}=\frac{n !(N-n) !}{N !}
$$

生物统计代考

统计代写|生物统计代写biostatistics代考|OBTAINING REPRESENTATIVE DATA

抽样的目的是获得足够数量的代表目标人群的数据，以便对目标人群的分布和参数进行统计推断。因为样本只是目标人群中单位的一个子集，一般无法保证样本数据能够代表目标人群；但是，通过精心设计的抽样计划，不太可能选择不代表目标人群的样本。为确保样本数据能够代表目标人群的可能性，必须考虑抽样过程的以下组成部分：

目标人群目标人群必须明确定义、易于访问，并且研究人员应对人群结构有很好的了解。特别是，研究人员应该能够识别总体单位、总体中单位的大致数量、亚总体、所研究变量分布的大致形状以及需要估计的相关参数。
抽样单位抽样单位是要抽样的总体单位。抽样单位可能是也可能不是人口的单位。事实上，在一些抽样计划中，抽样单位是人口单位的集合。抽样单位也是目标人群中可以选择的最小单位。
采样元件采样元件是将对其进行测量的对象。采样元件可以是也可以不是采样单元。当抽样单位由若干人口单位组成时，称为单位群。如果每个

将测量集群中的人口单位，然后抽样元素是抽样集群内的人口单位。在这种情况下，采样元素是采样单元的子单元。

抽样框架抽样框架是可用于抽样的抽样单位列表。抽样框架应该几乎等于目标人群。当抽样框架与目标人群显着不同时，即使采用精心设计的抽样计划，也不太可能获得代表目标人群的样本。未能包括目标总体的所有单位的抽样框架被称为隐藏目标总体，并可能导致样本有偏差。
样本大小样本大小是要选择的抽样单位的数量。样本大小将表示为n并且必须足够大以确保统计分析的可靠性。目标人群的可变性在确定与统计分析相关的所需可靠性水平所需的样本量方面起着关键作用。

统计代写|生物统计代写biostatistics代考|Probability Samples

为估计或检验关于总体参数的研究假设提供基础的统计理论基于称为概率抽样的抽样结构。概率样本是根据某种概率模型以随机方式选择的样本。具体而言，概率样本是这样选择的样本，使得预先知道每个可能的样本并且知道抽取每个采样单元的概率。随机样本是通过基于概率抽样的抽样计划产生的样本。

概率抽样允许抽样计划的灵活性，并且可以专门针对正在研究的目标人群进行设计。也就是说，概率抽样计划允许设计样本，使其不太可能产生不代表目标人群的样本。此外，概率样本允许从具有高度可靠性的观察样本中进行置信度陈述和假设检验。

方便样本是不基于概率样本的样本，也称为非概率样本。证明使用置信度陈述和假设检验的统计理论不适用于非概率样本；因此，基于非概率样本的研究假设的置信度陈述和检验是统计学的错误应用，不应被信任。
在随机样本中，人口中特定单位被选中的机会在抽样之前是已知的，并且可用于抽样的单位是根据这些概率随机选择的。抽取随机样本的过程概述如下。

统计代写|生物统计代写biostatistics代考|Simple Random Sampling

将要讨论的第一个抽样计划是简单随机抽样。一个简单的随机样本大小n是一个样本，由n抽样单位的选择方式使每一个可能的样本n单位有相同的机会被选中。在一个简单的随机样本中，每个可能的样本被选中的机会都是相同的，而且每个抽样单元在一个样本中被抽到的机会都是相同的。简单随机抽样是一种合理的抽样计划，用于对没有研究人员感兴趣的不同亚群的同质或异质人群进行抽样。
例 3.3
简单随机抽样在以下情况下可能是一个合理的抽样计划
：一家制药公司正在检查一种新药片剂的质量控制问题。在这里，该公司可能会从其最近生产的大量可用药片中随机抽取片剂样本。
湾。联邦食品和药物管理局 (FDA) 可能会对特定食品进行简单的随机抽样，以检查营养标签上信息的有效性。
C。一个州可能希望对医生进行简单的随机抽样，以审查该州的继续教育要求是否得到满足。
d。联邦或州环境机构可能希望对采矿城镇中的房屋进行简单的随机抽样，以调查该镇居民的总体健康状况以及采矿作业导致的房屋污染问题。

大小可能的简单随机样本数n从抽样框架列表中选择ñ抽样单位是

(ñ n)=ñ!n!(ñ−n)!
任意一个可能的简单随机样本的概率n从抽样框架中选择的单位ñ单位是

1ñ!n!(ñ−n)!=n!(ñ−n)!ñ!

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考| PROBABILITY MODELS

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考| PROBABILITY MODELS

统计代写|生物统计代写biostatistics代考|The Binomial Probability Model

The binomial probability model can be used for modeling the number of times a particular event occurs in a sequence of repeated trials. In particular, a binomial random variable is a discrete variable that is used to model chance experiments involving repeated dichotomous trials. That is, the binomial model is used to model repeated trials where the outcome of each trial is one of the two possible outcomes. The conditions under which the binomial probability model can be used are given below.

A random variable satisfying the above conditions is called a binomial random variable. Note that a binomial random variable $X$ simply counts the number of successes that occurred in $n$ trials. The probability distribution for a binomial random variable $X$ is given by the mathematical expression
$$
p(x)=\frac{n !}{x !(n-x) !} p^{x}(1-p)^{n-x} \quad \text { for } x=0,1, \ldots, n
$$
where $p(x)$ is the probability that $X$ is equal to the value $x$. In this formula

$\frac{n !}{x !(n-x) !}$ is the number of ways for there to be $x$ successes in $n$ trials,
$n !=n(n-1)(n-2) \cdots 3 \cdot 2 \cdot 1$ and $0 !=1$ by definition,
$p$ is the probability of a success on any of the $n$ trials,
$p^{x}$ is the probability of having $x$ successes in $n$ trials,
$1-p$ is the probability of a failure on any of the $n$ trials,
$(1-p)^{n-x}$ is the probability of getting $n-x$ failures in $n$ trials.
Examples of the binomial distribution are given in Figure 2.24. Note that a binomial distribution will have a longer tail to the right when $p<0.5$, a longer tail to the left when $p>0.5$, and is symmetric when $p=0.5$.

Because the computations for the probabilities associated with a binomial random variable are tedious, it is best to use a statistical computing package such as MINITAB for computing binomial probabilities.

统计代写|生物统计代写biostatistics代考|The Normal Probability Model

The choice of a probability model for continuous variables is generally based on historical data rather than a particular set of conditions. Just as there are many discrete probability models, there are also many different probability models that can be used to model the distribution of a continuous variable. The most commonly used continuous probability model in statistics is the normal probability model.

The normal probability model is often used to model distributions that are expected to be unimodal and symmetric, and the normal probability model forms the foundation for many of the classical statistical methods used in biostatistics. Moreover, the distribution of many natural phenomena can be modeled very well with the normal distribution. For example, the weights, heights, and IQs of adults are often modeled with normal distributions.

The standard normal, which will be denoted by $Z$, is a normal distribution having mean 0 and standard deviation 1. The standard normal is used as the reference distribution from which the probabilities and percentiles associated with any normal distribution will be determined. The cumulative probabilities for a standard normal are given in Tables A.1 and A.2; because $99.95 \%$ of the standard normal distribution lies between the values $-3.49$ and $3.49$, the standard normal values are only tabulated for $z$ values between $-3.49$ and $3.49$. Thus, when the value of a standard normal, say $z$, is between $-3.49$ and $3.49$, the tabled value for $z$ represents the cumulative probability of $z$, which is $P(Z \leq z)$ and will be denoted by $\Phi(z)$. For values of $z$ below $-3.50, \Phi(z)$ will be taken to be 0 and for values of $z$ above $3.50, \Phi(z)$ will be taken to be 1. Tables A.1 and A.2 can be used to compute all of the probabilities associated with a standard normal.

The values of $z$ are referenced in Tables A.1 and A.2 by writing $z=a . b c$ as $z=a . b+0.0 c$. To locate a value of $z$ in Table A.1 and A.2, first look up the value $a . b$ in the left-most column of the table and then locate $0.0 c$ in the first row of the table. The value cross-referenced by $a . b$ and $0 . c$ in Tables A.1 and A.2 is $\Phi(z)=P(Z \leq z)$. The rules for computing the probabilities for a standard normal are given below.

统计代写|生物统计代写biostatistics代考|Z Scores

The result of converting a non-standard normal value, a raw value, to a $Z$-value is a $Z$ score. A $Z$ score is a measure of the relative position a value has within its distribution. In particular, a $Z$ score simply measures how many standard deviations a point is above or below the mean. When a $Z$ score is negative the raw value lies below the mean of its distribution, and when a $Z$ score is positive the raw value lies above the mean. $Z$ scores are unitless measures of relative standing and provide a meaningful measure of relative standing only for mound-shaped distributions. Furthermore, $Z$ scores can be used to compare the relative standing of individuals in two mound-shaped distributions.
Example 2.41
The weights of men and women both follow mound-shaped distributions with different means and standard deviations. In fact, the weight of a male adult in the United States is approximately normal with mean $\mu=180$ and standard deviation $\sigma=30$, and the weight of a female adult in the United States is approximately normal with mean $\mu=145$ and standard deviation $\sigma=15$. Given a male weighing $215 \mathrm{lb}$ and a female weighing $170 \mathrm{lb}$, which individual weighs more relative to their respective population?

The answer to this question can be found by computing the $Z$ scores associated with each of these weights to measure their relative standing. In this case,
$$
z_{\text {male }}=\frac{215-180}{30}=1.17
$$
and
$$
z_{\text {female }}=\frac{170-145}{15}=1.67
$$
Since the female’s weight is $1.67$ standard deviations from the mean weight of a female and the male’s weight is $1.17$ standard deviations from the mean weight of a male, relative to their respective populations a female weighing $170 \mathrm{lb}$ is heavier than a male weighing $215 \mathrm{lb}$.

生物统计代考

统计代写|生物统计代写biostatistics代考|The Binomial Probability Model

二项式概率模型可用于对特定事件在一系列重复试验中发生的次数进行建模。特别是，二项式随机变量是一个离散变量，用于对涉及重复二分试验的随机试验进行建模。也就是说，二项式模型用于对重复试验进行建模，其中每次试验的结果是两种可能的结果之一。下面给出了可以使用二项式概率模型的条件。

满足上述条件的随机变量称为二项式随机变量。请注意，二项式随机变量X简单地计算发生的成功次数n试验。二项式随机变量的概率分布X由数学表达式给出

p(X)=n!X!(n−X)!pX(1−p)n−X 为了 X=0,1,…,n
在哪里p(X)是概率X等于值X. 在这个公式中

n!X!(n−X)!是有多少种方式X成功n试验，
n!=n(n−1)(n−2)⋯3⋅2⋅1和0!=1根据定义，
p是任何一个成功的概率n试验，
pX是拥有的概率X成功n试验，
1−p是任何一个失败的概率n试验，
(1−p)n−X是得到的概率n−X失败n试验。
图 2.24 给出了二项分布的示例。请注意，当二项分布的右尾较长时p<0.5, 一条较长的尾巴在左边时p>0.5, 并且是对称的p=0.5.

因为与二项式随机变量相关的概率的计算很繁琐，所以最好使用统计计算包，例如 MINITAB 来计算二项式概率。

统计代写|生物统计代写biostatistics代考|The Normal Probability Model

连续变量的概率模型的选择通常基于历史数据而不是特定的一组条件。正如有许多离散概率模型一样，也有许多不同的概率模型可用于对连续变量的分布进行建模。统计学中最常用的连续概率模型是正态概率模型。

正态概率模型通常用于对预期为单峰和对称的分布进行建模，并且正态概率模型构成了生物统计学中使用的许多经典统计方法的基础。此外，许多自然现象的分布可以用正态分布很好地建模。例如，成年人的体重、身高和智商通常采用正态分布建模。

标准法线，表示为从, 是具有均值 0 和标准偏差 1 的正态分布。标准正态用作参考分布，从中可以确定与任何正态分布相关的概率和百分位数。标准正态的累积概率在表 A.1 和 A.2 中给出；因为99.95%标准正态分布的值位于值之间−3.49和3.49, 标准正常值仅列出和之间的值−3.49和3.49. 因此，当标准法线的值时，比如说和，在。。。之间−3.49和3.49，表中的值为和表示累积概率和，即磷(从≤和)并将表示为披(和). 对于值和以下−3.50,披(和)将被取为 0 并且对于和以上3.50,披(和)将被视为 1。表 A.1 和 A.2 可用于计算与标准正态相关的所有概率。

的价值观和在表 A.1 和 A.2 中通过写入引用和=一个.bC作为和=一个.b+0.0C. 定位一个值和在表 A.1 和 A.2 中，首先查找值一个.b在表格的最左侧列中，然后找到0.0C在表格的第一行。交叉引用的值一个.b和0.C在表 A.1 和 A.2 中是披(和)=磷(从≤和). 下面给出了计算标准正态概率的规则。

统计代写|生物统计代写biostatistics代考|Z Scores

将非标准正常值（原始值）转换为从-值是从分数。一个从分数是一个值在其分布中的相对位置的度量。特别是，一个从分数只是衡量一个点高于或低于平均值的标准差。当一个从分数为负，原始值低于其分布的平均值，并且当从分数为正，原始值高于平均值。从分数是相对地位的无单位测量，并且仅对土墩形分布提供相对地位的有意义的测量。此外，从分数可用于比较两个土丘形分布中个体的相对地位。
示例 2.41
男性和女性的体重均遵循具有不同均值和标准差的土丘状分布。事实上，美国男性成年人的体重大约是正常的，平均μ=180和标准差σ=30, 美国成年女性的体重大致正常，平均μ=145和标准差σ=15. 给定一个男性称重215lb和一个称重的女性170lb，相对于他们各自的人口，哪个人的体重更大？

这个问题的答案可以通过计算从与这些权重中的每一个相关的分数以衡量它们的相对地位。在这种情况下，

和男性 =215−18030=1.17
和

和女性 =170−14515=1.67
由于女性的体重是1.67女性平均体重和男性体重的标准差为1.17男性平均体重的标准偏差，相对于他们各自的人口，女性体重170lb比男性称重215lb.

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|The Coefficient of Variation

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|The Coefficient of Variation

The standard deviations of two populations resulting from measuring the same variable can be compared to determine which of the two populations is more variable. That is, when one standard deviation is substantially larger than the other (i.e., more than two times as large), then clearly the population with the larger standard deviation is much more variable than the other. It is also important to be able to determine whether a single population is highly variable or not. A parameter that measures the relative variability in a population is the coefficient of variation. The coefficient of variation will be denoted by CV and is defined to be
$$
\mathrm{CV}=\frac{\sigma}{|\mu|}
$$
The coefficient of variation is also sometimes represented as a percentage in which case
$$
\mathrm{CV}=\frac{\sigma}{|\mu|} \times 100 \%
$$

The coefficient of variation compares the size of the standard deviation with the size of the mean. When the coefficient of variation is small, this means that the variability in the population is relatively small compared to the size of the mean of the population. On the other hand, when the coefficient of variation is large, this indicates that the population varies greatly relative to the size of the mean. The standard for what is a large coefficient of variation differs from one discipline to another, and in some disciplines a coefficient of variation of less than $15 \%$ is considered reasonable, and in other disciplines larger or smaller cutoffs are used.

Because the standard deviation and the mean have the same units of measurement, the coefficient of variation is a unitless parameter. That is, the coefficient is unaffected by changes in the units of measurement. For example, if a variable $X$ is measured in inches and the coefficient of variation is $\mathrm{CV}=2$, then coefficient of variation will also be 2 when the units of measurement are converted to centimeters. The coefficient of variation can also be used to compare the relative variability in two different and unrelated populations; the standard deviation can only be used to compare the variability in two different populations based on similar variables.

统计代写|生物统计代写biostatistics代考|Parameters for Bivariate Populations

In most biomedical research studies, there are many variables that will be recorded on each individual in the study. A multivariate distribution can be formed by jointly tabulating, charting, or graphing the values of the variables over the $N$ units in the population. For example, the bivariate distribution of two variables, say $X$ and $Y$, is the collection of the ordered pairs
$$
\left(X_{1}, Y_{1}\right),\left(X_{2}, Y_{2}\right),\left(X_{3}, Y_{3}\right), \ldots,\left(X_{N}, Y_{N}\right)
$$
These $N$ ordered pairs form the units of the bivariate distribution of $X$ and $Y$ and their joint distribution can be displayed in a two-way chart, table, or graph.

When the two variables are qualitative, the joint proportions in the bivariate distribution are often denoted by $p_{a b}$, where
$$
p_{a b}=\text { proportion of pairs in population where } X=a \text { and } Y=b
$$
The joint proportions in the bivariate distribution are then displayed in a two-way table or two-way bar chart. For example, according to the American Red Cross, the joint distribution of blood type and Rh factor is given in Table $2.7$ and presented as a bar chart in Figure $2.21$.

统计代写|生物统计代写biostatistics代考|Basic Probability Rules

Determining the probabilities associated with complex real-life events often requires a great deal of information and an extensive scientific understanding of the structure of the chance experiment being studied. In fact, even when the sample space and event are easily identified, the determination of the probability of an event can be an extremely difficult task. For example, in studying the side effects of a drug, the possible side effects can generally be anticipated and the sample space will be known. However, because humans react differently to drugs, the probabilities of the occurrence of the side effects are generally unknown. The probabilities of the side effects are often estimated in clinical trials.

The following basic probability rules are often useful in determining the probability of an event.

When the outcomes of a random experiment are equally likely to occur, the probability of an event $A$ is the number of outcomes in $A$ divided by the number of simple events in $\mathcal{S}$. That is,
$$
P(A)=\frac{\text { number of simple events in } A}{\text { number of simple events in } \mathcal{S}}=\frac{N(A)}{N(\delta)}
$$
For every event $A$, the probability of $A$ is the sum of the probabilities of the outcomes comprising $A$. That is, when an event $A$ is comprised of the outcomes $O_{1}, O_{2}, \ldots, O_{k}$, the probability of the event $A$ is
$$
P(A)=P\left(O_{1}\right)+P\left(O_{2}\right)+\cdots+P\left(O_{k}\right)
$$
For any two events $A$ and $B$, the probability that either event $A$ or event $B$ occurs is
$$
P(A \text { or } B)=P(A)+P(B)-P(A \text { and } B)
$$
The probability that the event $A$ does not occur is 1 minus the probability that the event $A$ does occur. That is,
$$
P(A \text { does not occur })=1-P(A)
$$

生物统计代考

统计代写|生物统计代写biostatistics代考|The Coefficient of Variation

可以比较由测量相同变量产生的两个总体的标准偏差，以确定两个总体中的哪一个更具可变性。也就是说，当一个标准差明显大于另一个时（即，两倍以上），那么显然具有较大标准差的总体比另一个具有更大的可变性。能够确定单个总体是否具有高度可变性也很重要。衡量总体相对变异性的参数是变异系数。变异系数用 CV 表示，定义为

C在=σ|μ|
变异系数有时也表示为百分比，在这种情况下

C在=σ|μ|×100%

变异系数将标准偏差的大小与平均值的大小进行比较。当变异系数较小时，这意味着总体的变异性与总体均值的大小相比相对较小。另一方面，当变异系数很大时，这表明总体相对于平均值的大小变化很大。大变异系数的标准因学科而异，在某些学科中，变异系数小于15%被认为是合理的，并且在其他学科中使用更大或更小的截止值。

因为标准差和平均值具有相同的测量单位，所以变异系数是一个无单位的参数。也就是说，系数不受测量单位变化的影响。例如，如果一个变量X以英寸为单位测量，变异系数为C在=2，那么当测量单位转换为厘米时，变异系数也将为 2。变异系数也可以用来比较两个不同且不相关的人群的相对变异性；标准差只能用于基于相似变量比较两个不同人群的变异性。

统计代写|生物统计代写biostatistics代考|Parameters for Bivariate Populations

在大多数生物医学研究中，研究中的每个人都会记录许多变量。多变量分布可以通过将变量的值联合制表、制图或绘图来形成ñ人口中的单位。例如，两个变量的二元分布，比如说X和是, 是有序对的集合

(X1,是1),(X2,是2),(X3,是3),…,(Xñ,是ñ)
这些ñ有序对形成二元分布的单位X和是并且它们的联合分布可以显示在双向图表、表格或图形中。

当两个变量是定性的时，双变量分布中的联合比例通常表示为p一个b，在哪里

p一个b= 人口中对的比例 X=一个和是=b
然后将双变量分布中的联合比例显示在双向表或双向条形图中。例如，根据美国红十字会，血型和Rh因子的联合分布如下表所示2.7并在图中显示为条形图2.21.

统计代写|生物统计代写biostatistics代考|Basic Probability Rules

确定与现实生活中复杂事件相关的概率通常需要大量信息和对所研究的偶然实验结构的广泛科学理解。事实上，即使样本空间和事件很容易识别，确定一个事件的概率也可能是一项极其困难的任务。例如，在研究药物的副作用时，通常可以预期可能的副作用，并且样本空间将是已知的。然而，由于人类对药物的反应不同，副作用发生的概率通常是未知的。通常在临床试验中估计副作用的概率。

以下基本概率规则通常可用于确定事件的概率。

当随机实验的结果同样可能发生时，事件发生的概率一个是结果的数量一个除以简单事件的数量小号. 那是，
磷(一个)= 简单事件的数量一个简单事件的数量小号=ñ(一个)ñ(d)
对于每一个事件一个, 的概率一个是结果的概率之和，包括一个. 也就是说，当一个事件一个由结果组成○1,○2,…,○ķ, 事件的概率一个是
磷(一个)=磷(○1)+磷(○2)+⋯+磷(○ķ)
对于任意两个事件一个和乙, 任一事件的概率一个或事件乙发生是
磷(一个或者乙)=磷(一个)+磷(乙)−磷(一个和乙)
事件发生的概率一个不发生是 1 减去事件发生的概率一个确实发生。那是，
磷(一个不发生 )=1−磷(一个)

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|Describing a Population with Parameters

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|Describing a Population with Parameters

统计代写|生物统计代写biostatistics代考|Proportions and Percentiles

Populations are often summarized by listing the important percentages or proportions associated with the population. The proportion of units in a population having a particular characteristic is a parameter of the population, and a population proportion will be denoted by $p$. The population proportion having a particular characteristic, say characteristic $A$, is defined to be
$$
p=\frac{\text { number of units in population having characteristic A }}{N}
$$
Note that the percentage of the population having characteristic A is $p \times 100 \%$. Population proportions and percentages are often associated with the categories of a qualitative variable or with the values in the population falling in a specific range of values. For example, the distribution of a qualitative variable is usually displayed in a bar chart with the height of a bar representing either the proportion or percentage of the population having that particular value.
Example 2.12
The distribution of blood type according to the American Red Cross is given in Table $2.4$ in terms of proportions.

An important proportion in many biomedical studies is the proportion of individuals having a particular disease, which is called the prevalence of the disease. The prevalence of a disease is defined to be
Prevalence $=$ The proportion of individuals in a well-defined population having the disease of interest
For example, according to the Centers for Disease Control and Prevention (CDC) the prevalence of smoking among adults in the United States in January through June 2005 was $20.9 \%$. Proportions also play important roles in the study of survival and cure rates, the occurrence of side effects of new drugs, the absolute and relative risks associated with a disease, and the efficacy of new treatments and drugs.

统计代写|生物统计代写biostatistics代考|Parameters Measuring Centrality

The two parameters in the population of values of a quantitative variable that summarize how the variable is distributed are the parameters that measure the typical or central values in the population and the parameters that measure the spread of the values within the population. Parameters describing the central values in a population and the spread of a population are often used for summarizing the distribution of the values in a population; however, it is important to note that most populations cannot be described very well with only the parameters that measure centrality and the spread of the population.

Measures of centrality, location, or the typical value are parameters that lie in the “center” or “middle” region of a distribution. Because the center or middle of a distribution is not easily determined due to the wide range of different shapes that are possible with a distribution, there are several different parameters that can be used to describe the center of a population. The three most commonly used parameters for describing the center of a population are the mean, median, and mode. For a quantitative variable $X$.

The mean of a population is the average of all of the units in the population, and will be denoted by $\mu$. The mean of a variable $X$ measured on a population consisting of $N$ units is
$$
\mu=\frac{\text { sum of the values of } X}{N}=\frac{\sum X}{N}
$$
The median of a population is the 50 th percentile of the population, and will be denoted by $\tilde{\mu}$. The median of a population is found by first listing all of the values of the variable $X$, including repeated $X$ values, in ascending order. When the number of units in the population (i.e., $N$ ) is an odd number, the median is the middle observation in the list of ordered values of $X$; when $N$ is an even number, the median will be the average of the two observations in the middle of the ordered list of $X$ values.
The mode of a population is the most frequent value in the population, and will be denoted by $M$. In a graph of the probability density function, the mode is the value of $X$ under the peak of the graph, and a population can have more than one mode as shown in Figure 2.8.

The mean, median, and mode are three different parameters that can be used to measure the center of a population or to describe the typical values in a population. These three parameters will have nearly the same value when the distribution is symmetric or mound shaped. For long-tailed distributions, the mean, median, and mode will be different, and the difference in their values will depend on the length of the distribution’s longer tail. Figures $2.12$ and $2.13$ illustrate the relationships between the values of the mean, median, and mode for long-tail right and long-tail left distributions.

统计代写|生物统计代写biostatistics代考|Measures of Dispersion

While the mean, median, and mode of a population describe the typical values in the population, these parameters do not describe how the population is spread over its range of values. For example, Figure $2.16$ shows two populations that have the same mean, median, and mode but different spreads.

Even though the mean, median, and mode of these two populations are the same, clearly, population I is much more spread out than population II. The density of population II is greater at the mean, which means that population II is more concentrated at this point than population I.

When describing the typical values in the population, the more variation there is in a population the harder it is to measure the typical value, and just as there are several ways of measuring the center of a population there are also several ways to measure the variation in a population. The three most commonly used parameters for measuring the spread of a population are the variance, standard deviation, and interquartile range. For a quantitative variable $X$

the variance of a population is defined to be the average of the squared deviations from the mean and will be denoted by $\sigma^{2}$ or $\operatorname{Var}(X)$. The variance of a variable $X$

measured on a population consisting of $N$ units is
$$
\sigma^{2}=\frac{\text { sum of all(deviations from } \mu)^{2}}{N}=\frac{\sum(X-\mu)^{2}}{N}
$$

the standard deviation of a population is defined to be the square root of the variance and will be denoted by $\sigma$ or $\operatorname{SD}(X)$.
$$
\operatorname{SD}(X)=\sigma=\sqrt{\sigma^{2}}=\sqrt{\operatorname{Var}(X)}
$$
the interquartile range of a population is the distance between the 25 th and 75 th percentiles and will be denoted by IQR.
$$
\mathrm{IQR}=75 \text { th percentile }-25 \text { th percentile }=X_{75}-X_{25}
$$

生物统计代考

统计代写|生物统计代写biostatistics代考|Proportions and Percentiles

人口通常通过列出与人口相关的重要百分比或比例来总结。人口中具有特定特征的单位的比例是人口的一个参数，人口比例将表示为p. 具有特定特征的人口比例，比如特征一个, 定义为

p= 人口中具有特征 A 的单位数 ñ
请注意，具有特征 A 的总体百分比是p×100%. 人口比例和百分比通常与定性变量的类别或人口中落在特定值范围内的值相关联。例如，定性变量的分布通常显示在条形图中，条形的高度代表具有该特定值的总体的比例或百分比。
例 2.12
美国红十字会血型分布见表2.4从比例上看。

在许多生物医学研究中，一个重要的比例是个体患有特定疾病的比例，这被称为疾病的患病率。疾病的患病率定义为
患病率=明确定义的人群中患有相关疾病的个体比例
例如，根据疾病控制和预防中心 (CDC) 的数据，2005 年 1 月至 2005 年 6 月美国成年人的吸烟率是20.9%. 比例在研究生存率和治愈率、新药副作用的发生、与疾病相关的绝对和相对风险以及新疗法和药物的疗效等方面也发挥着重要作用。

统计代写|生物统计代写biostatistics代考|Parameters Measuring Centrality

量化变量值总体中总结变量分布方式的两个参数是测量总体中的典型值或中心值的参数，以及测量值在总体中分布的参数。描述总体中的中心值和总体分布的参数通常用于总结总体中值的分布；然而，重要的是要注意，仅使用衡量中心性和人口分布的参数无法很好地描述大多数人口。

中心性、位置或典型值的度量是位于分布“中心”或“中间”区域的参数。由于分布可能具有多种不同形状，因此不容易确定分布的中心或中间，因此可以使用几个不同的参数来描述总体的中心。用于描述总体中心的三个最常用的参数是均值、中位数和众数。对于定量变量X.

总体的平均值是总体中所有单位的平均值，表示为μ. 变量的平均值X在由以下人员组成的总体上测量ñ单位是
μ= 的值的总和 Xñ=∑Xñ
人口的中位数是人口的第 50 个百分位，表示为μ~. 通过首先列出变量的所有值来找到总体的中位数X，包括重复X值，按升序排列。当人口中的单位数（即，ñ) 是奇数，中位数是的有序值列表中的中间观察值X; 什么时候ñ是偶数，中位数将是有序列表中间的两个观察值的平均值X价值观。
人口的众数是人口中出现频率最高的值，记为米. 在概率密度函数图中，众数是X如图 2.8 所示，一个总体可以有多个众数。

均值、中位数和众数是三个不同的参数，可用于衡量总体中心或描述总体中的典型值。当分布是对称或丘状时，这三个参数将具有几乎相同的值。对于长尾分布，均值、中位数和众数会有所不同，它们值的差异将取决于分布较长尾的长度。数字2.12和2.13说明长尾右分布和长尾左分布的均值、中值和众数之间的关系。

统计代写|生物统计代写biostatistics代考|Measures of Dispersion

虽然总体的平均值、中位数和众数描述了总体中的典型值，但这些参数并未描述总体在其值范围内的分布情况。例如，图2.16显示具有相同均值、中位数和众数但分布不同的两个总体。

尽管这两个总体的均值、中位数和众数相同，但显然，总体 I 比总体 II 更分散。人口 II 的平均密度更大，这意味着人口 II 在这一点上比人口 I 更集中。

在描述总体中的典型值时，总体中的变异越多，典型值的度量就越困难，正如度量一个总体的中心有多种方法一样，度量变异的方法也有多种在一个人口中。衡量总体分布的三个最常用的参数是方差、标准差和四分位距。对于定量变量X

总体的方差定义为与均值的平方偏差的平均值，并表示为σ2或者曾是⁡(X). 变量的方差X

在由以下人员组成的总体上测量ñ单位是

σ2= 所有的总和（偏离 μ)2ñ=∑(X−μ)2ñ

总体的标准差定义为方差的平方根，表示为σ或者标清⁡(X).
标清⁡(X)=σ=σ2=曾是⁡(X)
人口的四分位距是第 25 和第 75 个百分位数之间的距离，用 IQR 表示。
我问R=75 百分位数 −25 百分位数 =X75−X25

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|POPULATIONS AND VARIABLES

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|POPULATIONS AND VARIABLES

统计代写|生物统计代写biostatistics代考|Qualitative Variables

Qualitative variables take on nonnumeric values and are usually used to represent a distinct quality of a population unit. When the possible values of a qualitative variable have no intrinsic ordering, the variable is called a nominal variable; when there is a natural ordering of the possible values of the variable, then the variable is called an ordinal variable. An example of a nominal variable is Blood Type where the standard values for blood type are $\mathrm{A}, \mathrm{B}, \mathrm{AB}$, and $\mathrm{O}$. Clearly, there is no intrinsic ordering of these blood types, and hence, Blood Type is a nominal variable. An example of an ordinal variable is the variable Pain where a subject is asked to describe their pain verbally as

No pain,
Mild pain,
Discomforting pain,
Distressing pain,
Intense pain,
Excruciating pain.
In this case, since the verbal descriptions describe increasing levels of pain, there is a clear ordering of the possible values of the variable Pain levels, and therefore, Pain is an ordinal qualitative variable.
Example 2.2
In the Framingham Heart Study of coronary heart disease, the following two nominal qualitative variables were recorded:
$$
\text { Smokes }=\left{\begin{array}{l}
\text { Yes } \
\text { No }
\end{array}\right.
$$
and
$$
\text { Diabetes }=\left{\begin{array}{l}
\text { Yes } \
\text { No }
\end{array}\right.
$$
Example $2.3$
An example of an ordinal variable is the variable Baldness when measured on the Norwood-Hamilton scale for male-pattern baldness. The variable Baldness is measured according to the seven categories listed below:
I Full head of hair without any hair loss.
II Minor recession at the front of the hairline.
III Further loss at the front of the hairline, which is considered “cosmetically significant.”
IV Progressively more loss along the front hairline and at the crown.
V Hair loss extends toward the vertex.
VI Frontal and vertex balding areas merge into one and increase in size.
VII All hair is lost along the front hairline and crown.
Clearly, the values of the variable Baldness indicate an increasing degree of hair loss, and thus, Baldness as measured on the Norwood-Hamilton scale is an ordinal variable. This variable is also measured on the Offspring Cohort in the Framingham Heart Study.

统计代写|生物统计代写biostatistics代考|A quantitative variable

A quantitative variable is a variable that takes only numeric values. The values of a quantitative variable are said to be measured on an interval scale when the difference between two values is meaningful; the values of a quantitative variable are said to be measured on a ratio scale when the ratio of two values is meaningful. The key difference between a variable measured on an interval scale and a ratio scale is that on a ratio scale there is a “natural zero” representing absence of the attribute being measured, while there is no natural zero for variables measured on only an interval scale. Some scales of measurement will have natural zero and some will not. When a measurement scale has a natural zero, then the ratio of two measurements is a meaningful measure of how many times larger one value is than the other. For example, the variable Fat that represents the grams of fat in a food product is measured on a ratio scale because the value Fat $=0$ indicates that the unit contained absolutely no fat. When a scale of measurement does not have a natural zero, then only the difference between two measurements is a meaningful comparison of the values of the two measurements. For example, the variable Body Temperature is measured on a scale that has no natural zero since Body Temperature $=0$ does not indicate that the body has no temperature.

Since interval scales are ordered, the difference between two values measures how much larger one value is than another. A ratio scale is also an interval scale but has the additional property that the ratio of two values is meaningful. Thus, for a variable measured on an interval scale the difference of two values is the meaningful way to compare the values, and for a variable measured on a ratio scale both the difference and the ratio of two values are meaningful ways to compare difference values of the variable. For example, body temperature in degrees Fahrenheit is a variable that is measured on an interval scale so that it is meaningful to say that a body temperature of $98.6$ and a body temperature of $102.3$ differ by $3.7$ degrees; however, it would not be meaningful to say that a temperature of $102.3$ is $1.04$ times as much as a temperature of $98.6$. On the other hand, the variable weight in pounds is measured on a ratio scale, and therefore, it would be proper to say that a weight of $210 \mathrm{lb}$ is $1.4$ times a weight of $150 \mathrm{lb}$; it would also be meaningful to say that a weight of $210 \mathrm{lb}$ is $60 \mathrm{lb}$ more than a weight of $150 \mathrm{lb}$.

统计代写|生物统计代写biostatistics代考|Multivariate Data

In most research problems, there will be many variables that need to be measured. When the collection of variables measured on each unit consists of two or more variables, a data set is called a multivariate data set, and a multivariate data set consisting of only two variables is called a bivariate data set. In a multivariate data set, there is usually one variable that is of primary interest to a research question that is believed to be explained by some of the other variables measured in the study. The variable of primary interest is called a response variable and the variables believed to cause changes in the response are called explanatory variables or predictor variables. The explanatory variables are often referred to as the input variables and the response variable is often referred to as the output variable. Furthermore, in a statistical model, the response variable is the variable that is being modeled; the explanatory variables are the input variables in the model that are believed to cause or explain differences in the response variable. For example, in studying the survival of melanoma patients, the response variable might be Survival Time that is expected to be influenced by the explanatory variables Age, Gender, Clark’s Stage, and Tumor Size. In this case, a model relating Survival Time to the explanatory variables Age, Gender, Clark’s Stage, and Tumor Size might be investigated in the research study.

A multivariate data set often consists of a mixture of qualitative and quantitative variables. For example, in a biomedical study, several variables that are commonly measured are a subject’s age, race, gender, height, and weight. When data have been collected, the multivariate data set is generally stored in a spreadsheet with the columns containing the data on each variable and the rows of the spreadsheet containing the observations on each subject in the study.

In studying the response variable, it is often the case that there are subpopulations that are determined by a particular set of values of the explanatory variables that will be important in answering the research questions. In this case, it is critical that a variable be included in the data set that identifies which subpopulation each unit belongs to. For example, in the National Health and Nutrition Examination Survey (NHANES) study, the distribution of the weight of female children was studied. The response variable in this study was weight and some of the explanatory variables measured in this study were height, age, and gender. The result of this part of the NHANES study was a distribution of the weights of females over a certain range of age. The resulting distributions were summarized in the chart given in Figure $2.2$ that shows the weight ranges for females for several different ages.

生物统计代考

统计代写|生物统计代写biostatistics代考|Qualitative Variables

定性变量采用非数字值，通常用于表示人口单位的不同质量。当定性变量的可能值没有内在顺序时，该变量称为名义变量；当变量的可能值具有自然顺序时，该变量称为序数变量。名义变量的一个例子是血型，其中血型的标准值是一个,乙,一个乙，和○. 显然，这些血型没有内在的顺序，因此，血型是一个名义变量。序数变量的一个示例是变量疼痛，其中要求受试者口头描述他们的疼痛为

不痛，
轻微的疼痛，
令人不适的疼痛，
让人心疼的痛，
剧烈的疼痛，
难以忍受的疼痛。
在这种情况下，由于口头描述描述了疼痛程度的增加，因此变量疼痛水平的可能值有一个明确的顺序，因此，疼痛是一个有序的定性变量。
例 2.2
在冠心病的弗雷明汉心脏研究中，记录了以下两个名义上的定性变量：
$$
\text { Smokes }=\left{ 是的不 \正确的。
$$
和
$$
\text { 糖尿病 }=\left{\begin{array}{l}
\文本{是} \
\文本{没有}
\end{数组}\对。
$$
例子2.3
序数变量的一个例子是变量 Baldness，当用 Norwood-Hamilton 量表测量男性型秃发时。变量秃头根据以下列出的七个类别进行测量：
我满头的头发没有任何脱发。
II 发际线前部的轻微后退。
III 发际线前部的进一步损失，这被认为是“具有美容意义的”。
IV 沿着前发际线和头顶逐渐减少。
V 脱发向顶点延伸。
VI 前额和头顶秃发区域合并为一个并增加大小。
VII 所有的头发都沿着前发际线和头顶脱落。
显然，变量秃头的值表明脱发程度的增加，因此，在诺伍德-汉密尔顿量表上测量的秃头是一个序数变量。这个变量也在弗雷明汉心脏研究的后代队列中测量。

统计代写|生物统计代写biostatistics代考|A quantitative variable

定量变量是只取数值的变量。当两个值之间的差异有意义时，就说定量变量的值是在区间尺度上测量的；当两个值的比率有意义时，就可以说定量变量的值是在比率尺度上测量的。在区间尺度和比率尺度上测量的变量之间的主要区别在于，在比率尺度上，有一个“自然零”表示不存在被测量的属性，而仅在区间尺度上测量的变量没有自然零. 一些测量尺度将具有自然零，而一些则没有。当测量尺度具有自然零时，两个测量值的比率是一个有意义的度量，用于衡量一个值比另一个值大多少倍。例如，=0表示该单位绝对不含脂肪。当测量尺度没有自然零时，只有两次测量之间的差异才是两次测量值的有意义的比较。例如，变量体温是在一个没有自然零的标度上测量的，因为体温=0并不表示身体没有温度。

由于区间尺度是有序的，因此两个值之间的差值衡量一个值比另一个值大多少。比率刻度也是一个区间刻度，但具有两个值的比率有意义的附加属性。因此，对于在区间尺度上测量的变量，两个值的差异是比较值的有意义的方式，而对于在比率尺度上测量的变量，两个值的差异和比率都是比较差异值的有意义的方式变量。例如，以华氏度为单位的体温是一个在区间尺度上测量的变量，因此说体温为98.6和体温102.3区别于3.7学位；然而，说温度为102.3是1.04温度的几倍98.6. 另一方面，以磅为单位的可变重量是在比例尺度上测量的，因此，可以说重量为210lb是1.4重量的倍150lb; 说一个重量210lb是60lb超过一个重量150lb.

统计代写|生物统计代写biostatistics代考|Multivariate Data

在大多数研究问题中，都会有很多变量需要衡量。当在每个单元上测量的变量集合由两个或多个变量组成时，一个数据集称为多变量数据集，仅由两个变量组成的多变量数据集称为二元数据集。在多变量数据集中，通常有一个变量对研究问题具有主要兴趣，据信该变量可以通过研究中测量的其他一些变量来解释。主要关注的变量称为响应变量，而被认为导致响应变化的变量称为解释变量或预测变量。解释变量通常称为输入变量，响应变量通常称为输出变量。此外，在统计模型中，响应变量是正在建模的变量；解释变量是模型中被认为导致或解释响应变量差异的输入变量。例如，在研究黑色素瘤患者的生存情况时，响应变量可能是预计受解释变量年龄、性别、克拉克分期和肿瘤大小影响的生存时间。在这种情况下，可以在研究中研究将生存时间与解释变量年龄、性别、克拉克阶段和肿瘤大小相关联的模型。在研究黑色素瘤患者的生存情况时，响应变量可能是预计受解释变量年龄、性别、克拉克分期和肿瘤大小影响的生存时间。在这种情况下，可以在研究中研究将生存时间与解释变量年龄、性别、克拉克阶段和肿瘤大小相关联的模型。在研究黑色素瘤患者的生存情况时，响应变量可能是预计受解释变量年龄、性别、克拉克分期和肿瘤大小影响的生存时间。在这种情况下，可以在研究中研究将生存时间与解释变量年龄、性别、克拉克阶段和肿瘤大小相关联的模型。

多变量数据集通常由定性和定量变量的混合组成。例如，在生物医学研究中，通常测量的几个变量是受试者的年龄、种族、性别、身高和体重。收集数据后，多变量数据集通常存储在电子表格中，其中列包含每个变量的数据，电子表格的行包含研究中每个受试者的观察结果。

在研究响应变量时，通常存在由一组特定的解释变量值确定的子群体，这些解释变量对回答研究问题很重要。在这种情况下，关键是要在数据集中包含一个变量，以识别每个单元属于哪个亚群。例如，在全国健康和营养检查调查 (NHANES) 研究中，研究了女童的体重分布。本研究中的响应变量是体重，本研究中测量的一些解释变量是身高、年龄和性别。NHANES 研究的这一部分的结果是女性在一定年龄范围内的体重分布。得到的分布总结在图中给出的图表中2.2这显示了几个不同年龄的女性的体重范围。

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

非参数统计代写

非参数统计指的是一种统计方法，其中不假设数据来自于由少数参数决定的规定模型；这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型（GLM）归属统计学领域，是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

有限元方法代写

随机分析代写

时间序列分析代写

回归分析代写

MATLAB代写

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写

统计代写|生物统计代写biostatistics代考|DESCRIBING POPULATIONS

Posted on 2022年6月16日2022年6月16日 by statistics-lab

如果你也在怎样代写生物统计biostatistics这个学科遇到相关的难题，请随时右上角联系我们的24/7代写客服。

生物统计学是将统计技术应用于健康相关领域的科学研究，包括医学、生物学和公共卫生，并开发新的工具来研究这些领域。

我们提供的生物统计biostatistics及其相关学科的代写，服务范围广, 其中包括但不限于:

Statistical Inference 统计推断
Statistical Computing 统计计算
Advanced Probability Theory 高等概率论
Advanced Mathematical Statistics 高等数理统计学
(Generalized) Linear Models 广义线性模型
Statistical Machine Learning 统计机器学习
Longitudinal Data Analysis 纵向数据分析
Foundations of Data Science 数据科学基础

统计代写|生物统计代写biostatistics代考|DESCRIBING POPULATIONS

统计代写|生物统计代写biostatistics代考|The Phases of a Clinical Trial

Clinical research is often conducted in a series of steps, called phases. Because a new drug, medicine, or treatment must be safe, effective, and manufactured at a consistent quality, a series of rigorous clinical trials are usually required before the drug, medicine, or treatment can be made available to the general public. In the United States the FDA regulates and oversees the testing and approval of new drugs as well as dietary supplements, cosmetics, medical devices, blood products, and the content of health claims on food labels. The approval of a new drug by the FDA requires extensive testing and evaluation of the drug through a series of four clinical trials, which are referred to as phase $I, I I, I I I$, and $I V$ trials.
Each of the four phases is designed with a different purpose and to provide the necessary information to help biomedical researchers answer several different questions about

a new drug, treatment, or biomedical procedure. After a clinical trial is completed, the researchers use biostatistical methods to analyze the data collected during the trial and make decisions and draw conclusions about the meaning of their findings and whether further studies are needed. After each phase in the study of a new drug or treatment, the research team must decide whether to proceed to the next phase or stop the investigation of the drug/treatment. Formal approval of a new drug or biomedical procedure generally cannot be made until a phase III trial is completed and there is strong evidence that the drug/treatment is safe and effective.

The purpose of a phase $I$ clinical trial is to investigate the safety, efficacy, and side effects of a new drug or treatment. Phase I trials usually involve a small number of subjects and take place at a single or only a few different locations. In a drug trial, the goal of a phase I trial is often to investigate the metabolic and pharmacologic actions of the drug, the efficacy of the drug, and the side effects associated with different dosages of the drug. Phase I drug trials are also referred to as dose finding trials.

统计代写|生物统计代写biostatistics代考|POPULATIONS AND VARIABLES

In a properly designed biomedical research study, a well-defined target population and a particular set of research questions dictate the variables that should be measured on the units being studied in the research project. In most research problems, there are many variables

that must be measured on each unit in the population. The outcome variables that are of primary interest are called the response variables, and the variables that are believed to explain the response variables are called the explanatory variables or predictor variables. For example, in a clinical trial designed to study the efficacy of a specialized treatment designed to reduce the size of a malignant tumor, the following explanatory variables might be recorded for each patient in the study: age, gender, race, weight, height, blood type, blood pressure, and oxygen uptake. The response variable in this study might be change in the size of the tumor.

Variables come in a variety of different types; however, each variable can be classified as being either quantitative or qualitative in nature. A variable that takes on only numeric values is a quantitative variable, and a variable that takes on non-numeric values is called a qualitative variable or a categorical variable. Note that a variable is a quantitative or qualitative variable based on the possible values the variable can take on.
Example $2.1$
In a study of obesity in the population of children aged 10 or less in the United States, some possible quantitative variables that might be measured include age, height, weight, heart rate, body mass index, and percent body fat; some qualitative variables that might be measured on this population include gender, eye color, race, and blood type. A likely choice for the response variable in this study would be the qualitative variable Obese defined by
$$
\text { Obese }= \begin{cases}\text { Yes } & \text { for a body mass index of }>30 \ \text { No } & \text { for a body mass index of } \leq 30\end{cases}
$$

统计代写|生物统计代写biostatistics代考|Qualitative Variables

No pain,
Mild pain,
Discomforting pain,
Distressing pain,
Intense pain,
Excruciating pain.
In this case, since the verbal descriptions describe increasing levels of pain, there is a clear ordering of the possible values of the variable Pain levels, and therefore, Pain is an ordinal qualitative variable.
Example 2.2
In the Framingham Heart Study of coronary heart disease, the following two nominal qualitative variables were recorded:
$$
\text { Smokes }=\left{\begin{array}{l}
\text { Yes } \
\text { No }
\end{array}\right.
$$
and
$$
\text { Diabetes }=\left{\begin{array}{l}
\text { Yes } \
\text { No }
\end{array}\right.
$$

生物统计代考

统计代写|生物统计代写biostatistics代考|The Phases of a Clinical Trial

临床研究通常分一系列步骤进行，称为阶段。由于新药、新药或新疗法必须安全、有效并以一致的质量生产，因此通常需要进行一系列严格的临床试验，然后才能向公众提供该新药、新药或新疗法。在美国，FDA 监管和监督新药以及膳食补充剂、化妆品、医疗器械、血液制品以及食品标签上的健康声明内容的测试和批准。FDA批准一种新药需要通过一系列四项临床试验对药物进行广泛的测试和评估，这被称为阶段我,我我,我我我，和我在试验。
四个阶段中的每一个都具有不同的目的，并提供必要的信息来帮助生物医学研究人员回答关于

一种新的药物、治疗或生物医学程序。临床试验完成后，研究人员使用生物统计学方法分析试验期间收集的数据，并就其发现的意义以及是否需要进一步研究做出决策并得出结论。在新药或治疗研究的每个阶段之后，研究团队必须决定是继续下一阶段还是停止对该药物/治疗的研究。新药或生物医学程序的正式批准通常要等到 III 期试验完成并且有强有力的证据表明该药物/治疗是安全有效的。

阶段的目的我临床试验是调查一种新药或治疗方法的安全性、有效性和副作用。I 期试验通常涉及少数受试者，并在一个或几个不同的地点进行。在药物试验中，I 期试验的目标通常是研究药物的代谢和药理作用、药物的功效以及与药物不同剂量相关的副作用。I 期药物试验也称为剂量发现试验。

统计代写|生物统计代写biostatistics代考|POPULATIONS AND VARIABLES

在适当设计的生物医学研究中，明确定义的目标人群和一组特定的研究问题决定了应该在研究项目中研究的单位上测量的变量。在大多数研究问题中，存在许多变量

必须对人口中的每个单位进行衡量。主要感兴趣的结果变量称为响应变量，而被认为可以解释响应变量的变量称为解释变量或预测变量。例如，在一项旨在研究旨在减少恶性肿瘤大小的专门治疗的功效的临床试验中，可能会为研究中的每位患者记录以下解释变量：年龄、性别、种族、体重、身高、血型、血压和摄氧量。本研究中的反应变量可能是肿瘤大小的变化。

变量有多种不同的类型；但是，每个变量本质上都可以分为定量或定性。只取数值的变量称为定量变量，取非数值的变量称为定性变量或分类变量。请注意，变量是基于变量可以采用的可能值的定量或定性变量。
例子2.1
在一项针对美国 10 岁或以下儿童人群的肥胖研究中，一些可能测量的定量变量包括年龄、身高、体重、心率、体重指数和体脂百分比；可以在该人群中测量的一些定性变量包括性别、眼睛颜色、种族和血型。本研究中响应变量的一个可能选择是定性变量肥胖，定义为

肥胖 ={ 是的对于体重指数 >30 不对于体重指数 ≤30

统计代写|生物统计代写biostatistics代考|Qualitative Variables

不痛，
轻微的疼痛，
令人不适的疼痛，
让人心疼的痛，
剧烈的疼痛，
难以忍受的疼痛。
在这种情况下，由于口头描述描述了疼痛程度的增加，因此变量疼痛水平的可能值有一个明确的顺序，因此，疼痛是一个有序的定性变量。
例 2.2
在冠心病的弗雷明汉心脏研究中，记录了以下两个名义上的定性变量：
$$
\text { Smokes }=\left{ 是的不 \正确的。
$$
和
$$
\text { 糖尿病 }=\left{\begin{array}{l}
\文本{是} \
\文本{没有}
\end{数组}\对。
$$

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

R语言代写	问卷设计与分析代写
PYTHON代写	回归分析与线性模型代写
MATLAB代写	方差分析与试验设计代写
STATA代写	机器学习/统计学习代写
SPSS代写	计量经济学代写
EVIEWS代写	时间序列分析代写
EXCEL代写	深度学习代写
SQL代写	各种数据建模与可视化代写