统计代写|统计推断作业代写statistical inference代考|CDF and survival function

statistics-lab™ 为您的留学生涯保驾护航 在代写 统计推断statistical inference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。我们的专家在代写统计推断statistical inference方面经验极为丰富，各种代写 统计推断statistical inference相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• Advanced Probability Theory 高等楖率论
• 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|统计推断作业代写statistical inference代考|CDF and survival function

Certain areas of PDFs and PMFs are so useful, we give them names. The cumulative distribution function (CDF) of a random variable, $X$, returns the probability that the random variable is less than or equal to the value $x$. Notice the (slightly annoying) convention that we use an upper case $X$ to denote a random, unrealized, version of the random variable and a lowercase $x$ to denote a specific number that we plug into. (This notation, as odd as it may seem, dates back to Fisher and isn’t going anywhere, so you might as well get used to it. Uppercase for unrealized random variables and lowercase as placeholders for numbers to plug into.) So we could write the following to describe the distribution function $F$ :
$$F(x)=P(X \leq x)$$
This definition applies regardless of whether the random variable is discrete or continuous. The survival function of a random variable $X$ is defined as the probability that the random variable is greater than the value $x$.
$S(x)=P(X>x)$
Notice that $S(x)=1-F(x)$, since the survival function evaluated at a particular value of $x$ is calculating the probability of the opposite event (greater than as opposed to less than or equal to). The survival function is often preferred in biostatistical applications while the distribution function is more generally used (though both convey the same information.)

统计代写|统计推断作业代写statistical inference代考|Example

What are the survival function and CDF from the density considered before?
$$F(x)=P(X \leq x)=\frac{1}{2} \text { Base } \times \text { Height }=\frac{1}{2}(x) \times(2 x)=x^{2},$$
for $1 \geq x \geq 0$. Notice that calculating the survival function is now trivial given that we’ve already calculated the distribution function.
$S(x)=1=F(x)=1-x^{2}$
Again, $\mathrm{R}$ has a function that calculates the distribution function for us in this case, pbeta. Let’s try calculating $F(.4), F(.5)$ and $F(.6)$
3 phataçc(ด.4, ด. ร, ด. ค), 3,1$)$
[1] $0.16 \quad 0.25 \quad 0.36$
Notice, of course, these are simply the numbers squared. By default the prefix $p$ in front of a density in R gives the distribution function (pbeta, pnorm, pgamma). If you want the survival function values, you could always subtract by one, or give the argument lower.tail = FALSE as an argument to the function, which asks $R$ to calculate the upper area instead of the lower.

统计代写|统计推断作业代写statistical inference代考|Quantiles

You’ve heard of sample quantiles. If you were the 95 th percentile on an exam, you know that $95 \%$ of people scored worse than you and $5 \%$ scored better. These are sample quantities. But you might have wondered, what are my sample quantiles estimating? In fact, they are estimating the population quantiles. Here we define these population analogs.

The $\alpha^{t h}$ quantile of a distribution with distribution function $F$ is the point $x_{\alpha}$ so that
$$F\left(x_{\alpha}\right)=\alpha$$
So the $0.95$ quantile of a distribution is the point so that $95 \%$ of the mass of the density lies below it. Or, in other words, the point so that the probability of getting a randomly sampled point below it is $0.95$. This is analogous to the sample quantiles where the $0.95$ sample quantile is the value so that $95 \%$ of the data lies below it.
A percentile is simply a quantile with $\alpha$ expressed as a percent rather than a proportion. The (population) median is the $50^{t h}$ percentile. Remember that percentiles are not probabilities! Remember that quantiles have units. So the population median height is the height (in inches say) so that the probability that a randomly selected person from the population is shorter is $50 \%$. The sample, or empirical, median would be the height so in a sample so that $50 \%$ of the people in the sample were shorter.

统计代写|统计推断作业代写statistical inference代考|CDF and survival function

PDF 和 PMF 的某些领域非常有用，我们给它们命名。随机变量的累积分布函数 (CDF)，X, 返回随机变量小于或等于该值的概率X. 注意我们使用大写的（有点烦人的）约定X表示随机变量的一个随机的、未实现的版本和一个小写字母X表示我们插入的特定数字。（这个符号，虽然看起来很奇怪，但可以追溯到 Fisher 并且不会出现在任何地方，所以你不妨习惯它。大写表示未实现的随机变量，小写表示插入数字的占位符。）所以我们可以写出以下来描述分布函数F :
F(X)=磷(X≤X)

统计代写|统计推断作业代写statistical inference代考|Example

F(X)=磷(X≤X)=12 根据 × 高度 =12(X)×(2X)=X2,

3 phataçc(Dor.4,Dor.Ror.,Dor.C.), 3,1)
[1] 0.160.250.36

F(X一种)=一种

广义线性模型代考

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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。