### 统计代写|应用时间序列分析代写applied time series analysis代考|DISTRIBUTIONAL PROPERTIES OF RETURNS

statistics-lab™ 为您的留学生涯保驾护航 在代写应用时间序列分析applied time series analysis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。我们的专家在代写应用时间序列分析applied time series analysis方面经验极为丰富，各种代写应用时间序列分析applied time series analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|应用时间序列分析代写applied time series anakysis代考|Review of Statistical Distributions and Their Moments

We briefly review some basic properties of statistical distributions and the moment equations of a random variable. Let $R^{k}$ be the $k$-dimensional Euclidean space. A point in $R^{k}$ is denoted by $\boldsymbol{x} \in R^{k}$. Consider two random vectors $\boldsymbol{X}=\left(X_{1}, \ldots, X_{k}\right)^{\prime}$ and $\boldsymbol{Y}=\left(Y_{1}, \ldots, Y_{q}\right)^{\prime}$. Let $P(\boldsymbol{X} \in A, \boldsymbol{Y} \in B)$ be the probability that $\boldsymbol{X}$ is in the subspace $A \subset R^{k}$ and $Y$ is in the subspace $B \subset R^{q}$. For most of the cases considered in this book, both random vectors are assumed to be continuous.

The function
$$F_{X, Y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta})=P(\boldsymbol{X} \leq \boldsymbol{x}, \boldsymbol{Y} \leq \boldsymbol{y})$$
where $\boldsymbol{x} \in R^{p}, \boldsymbol{y} \in R^{q}$, and the inequality ” $\leq$ ” is a component-by-component operation, is a joint distribution function of $\boldsymbol{X}$ and $\boldsymbol{Y}$ with parameter $\boldsymbol{\theta}$. Behavior of $X$ and $Y$ is characterized by $F_{X, Y}(x, y ; \theta)$. If the joint probability density function $f_{x, y}(x, y ; \theta)$ of $X$ and $Y$ exists, then
$$F_{X, Y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta})=\int_{-\infty}^{x} \int_{-\infty}^{y} f_{x, y}(w, z ; \theta) d z d w$$
In this case, $\boldsymbol{X}$ and $\boldsymbol{Y}$ are continuous random vectors.

## 统计代写|应用时间序列分析代写applied time series anakysis代考| Marginal Distribution

The marginal distribution of $X$ is given by
$$F_{X}(x, \theta)=F_{X, Y}(\boldsymbol{x}, \infty, \ldots, \infty ; \theta)$$
Thus, the marginal distribution of $X$ is obtained by integrating out $Y$. A similar definition applies to the marginal distribution of $\boldsymbol{Y}$.
If $k=1, X$ is a scalar random variable and the distribution function becomes
$$F_{X}(x)=P(X \leq x ; \theta)$$
which is known as the cumulative distribution function (CDF) of $X$. The CDF of a random variable is nondecreasing [i.e., $F_{X}\left(x_{1}\right) \leq F_{X}\left(x_{2}\right)$ if $x_{1} \leq x_{2}$, and satisfies $F_{X}(-\infty)=0$ and $\left.F_{X}(\infty)=1\right]$. For a given probability $p$, the smallest real number $x_{p}$ such that $p \leq F_{X}\left(x_{p}\right)$ is called the $p$ th quantile of the random variable $X$. More specifically,
$$x_{p}=\inf {X}\left{x \mid p \leq F{X}(x)\right}$$
We use CDF to compute the $p$ value of a test statistic in the book.

## 统计代写|应用时间序列分析代写applied time series anakysis代考| Conditional Distribution

The conditional distribution of $X$ given $Y \leq y$ is given by
$$F_{X \mid Y \leq y}(\boldsymbol{x} ; \boldsymbol{\theta})=\frac{P(\boldsymbol{X} \leq \boldsymbol{x}, \boldsymbol{Y} \leq \boldsymbol{y})}{P(\boldsymbol{Y} \leq \boldsymbol{y})}$$
If the probability density functions involved exist, then the conditional density of $\boldsymbol{X}$ given $Y=y$ is

$$f_{x \mid y}(\boldsymbol{x} ; \boldsymbol{\theta})=\frac{f_{x, y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta})}{f_{y}(\boldsymbol{y} ; \boldsymbol{\theta})}$$
where the marginal density function $f_{y}(y ; \theta)$ is obtained by
$$f_{y}(\boldsymbol{y} ; \boldsymbol{\theta})=\int_{-\infty}^{\infty} f_{x, y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta}) d \boldsymbol{x}$$
From Eq. (1.8), the relation among joint, marginal, and conditional distributions is
$$f_{x, y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta})=f_{x \mid y}(\boldsymbol{x} ; \boldsymbol{\theta}) \times f_{y}(\boldsymbol{y} ; \boldsymbol{\theta})$$
This identity is used extensively in time series analysis (e.g., in maximum likelihood estimation). Finally, $\boldsymbol{X}$ and $\boldsymbol{Y}$ are independent random vectors if and only if $f_{x \mid y}(\boldsymbol{x} ; \boldsymbol{\theta})=f_{x}(\boldsymbol{x} ; \boldsymbol{\theta})$. In this case, $f_{x, y}(\boldsymbol{x}, \boldsymbol{y} ; \boldsymbol{\theta})=f_{x}(\boldsymbol{x} ; \boldsymbol{\theta}) f_{y}(\boldsymbol{y} ; \boldsymbol{\theta})$.

## 统计代写|应用时间序列分析代写applied time series anakysis代考|Review of Statistical Distributions and Their Moments

FX,是(X,是;θ)=磷(X≤X,是≤是)

FX,是(X,是;θ)=∫−∞X∫−∞是FX,是(在,和;θ)d和d在

## 统计代写|应用时间序列分析代写applied time series anakysis代考| Marginal Distribution

FX(X,θ)=FX,是(X,∞,…,∞;θ)

FX(X)=磷(X≤X;θ)

x_{p}=\inf {X}\left{x \mid p \leq F{X}(x)\right}x_{p}=\inf {X}\left{x \mid p \leq F{X}(x)\right}

## 统计代写|应用时间序列分析代写applied time series anakysis代考| Conditional Distribution

FX∣是≤是(X;θ)=磷(X≤X,是≤是)磷(是≤是)

F是(是;θ)=∫−∞∞FX,是(X,是;θ)dX

FX,是(X,是;θ)=FX∣是(X;θ)×F是(是;θ)

## 广义线性模型代考

statistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

## 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。