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assignmentutor-lab™ 为您的留学生涯保驾护航 在代写随机控制Stochastic Control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。我们的专家在代写随机控制Stochastic Control代写方面经验极为丰富，各种代写随机控制Stochastic Control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|随机控制代写Stochastic Control代考|Creating Probability Plots

Probability plots are graphical expressions used in examining data structures. Plots provide insights into the suitability of a particular probability density function (pdf) in describing the stochastic behavior of the data and estimates of the unknown parameters of the pdf. Although generally very powerful, the inferences drawn from probability plots are subjective.
The underlying principle behind probability plots is simple and consistent. The order statistics, with $Y_{[i]}$ denoting the ith largest observation, such that
$$Y_{[1]} \leq Y_{[2]} \leq \ldots \leq Y_{[i]} \leq \ldots \leq Y_{[n]}$$
are plotted versus their expected values $E\left(Y_{[i]}\right)$. A linear relationship between the order statistics and their expected values indicates the pdf used in determining the expected values provides a reasonable representation of the behavior of the observed data. A non-linear plot suggests that other pdf(s) may be more suitable in describing the stochastic structure of the data.
The expected value of the ith order statistic is
$$E\left(Y_{[i]}\right)=n ! /[(i-1) !(n-i) !] \int_0^1 Y_{[i]}\left[F\left(y_{[i]}\right)\right]^{(i-1)}\left[1-F\left(y_{[i]}\right)\right]^{(n-i)} d F\left(y_{[i]}\right)$$

where $\mathrm{f}(\mathrm{y})$ denotes the pdf being considered, $\mathrm{F}(\mathrm{y})$ the associated cumulative distribution function (cdf) and $\mathrm{n}$ the size of the dataset under investigation. Because numerical solutions for this equation can be difficult, the approximation $E\left(Y_{[i]}\right)=F^{-1}[(i-c) /(n-2 c-1)]$, where $F^{-1}$ denotes the inverse $c d f$ and $c$ a constant $(0 \leq c \leq 1)$ is frequently used. Setting $c=0.5$ (for discussion see Kimball (1960)) results in
$$E\left(Y_{[i]}\right)=F^{-1}[(i-0.5) / n]$$
and is the approximation used here. Mathematica will be used to evaluate the $E\left(Y_{[i]}\right)$, create the resulting probability plot, assist in assessing linearity and determine parameter estimates.
Mathematica’s Quantile functions are used to find the $E\left(Y_{[i]}\right)^{\prime}$ s for specific pdfs and create the plot of $Y_{[i]}$ versus $E\left(Y_{[i]}\right)$. If the resulting plot is considered linear then the pdf used to determine the $E\left(Y_{[i]}\right)^{\prime}$ s can be used to describe the stochastic structure of the data. Assuming the plot is deemed linear, estimates for the unknown parameters can be determined from the plot.

## 统计代写|随机控制代写Stochastic Control代考|Creating & Interpreting 3-D Probability Surfaces

Dynamic graphic techniques have opened new frontiers in data display and analysis. With a basic understanding of simple probability plots, subjective interpretation of distributional assumptions can be made for families of distributions that contain a shape parameter. Strong visual results are possible for relatively small sample sizes. In the examples that follow, sample sizes of 25 provide good insights into the distributional properties of the observed data.

Let $\mathrm{Y}$ denote a random variable with pdf $\mathrm{f}(\mathrm{y} ; \mu, \sigma, \lambda)$ and $\operatorname{cdf} \mathrm{F}(\mathrm{y} ; \mu, \sigma, \lambda)$ where $\mu, \sigma$ and $\lambda$ denote the location, scale and shape parameters of the distribution respectively. Cheng and Spiring (1990) defined the X-axis as $E\left(Y_{[i]} ; \lambda\right)$, scaled the Z-axis arithmetically and defined it as the order statistics $Y_{[i]}$ and let the $Y$ axis denote values of the shape parameter $\lambda$, to create a surface in 3 space. Examination of the resulting surface allowed inferences regarding the stochastic nature of the data as well as estimates for location, scale and shape parameters of the associated pdf.

The resulting surface is essentially an infinite number of traditional probability plots laid side by side. These probability plots are ordered by the value of the shape parameter used in calculating the $E\left(Y_{[i]}\right)^{\prime}$ s. Slicing the surface along planes parallel to the $\mathrm{XZ}$ plane at various points along the $Y$ axis, allows viewing of the “linearity” of the surface by considering the resultant projection on the $\mathrm{XZ}$ plane. The projection is a univariate probability plot of the data for a particular value of the shape parameter. The goal then is to slice the surface such that the most linear projection on the XZ plane is found.

Rotation allows viewing of the created surface from several perspectives, enhancing the ability to determine where the surface appears most linear and the associated value of the shape parameter. From the most linear portion of the surface, estimates for the location, scale and shape parameters can be determined. The 50 th percentile (or midpoint of the $\mathrm{X}$-axis provides an estimate for the location, the value of the Y-axis where the surface is most linear provides an estimate for the shape parameter and the slope of the surface (in the X-direction) an estimate of the scale.

## 统计代写|随机控制代写Stochastic Control代考|创建概率图

$$Y_{[1]} \leq Y_{[2]} \leq \ldots \leq Y_{[i]} \leq \ldots \leq Y_{[n]}$$

$$E\left(Y_{[i]}\right)=n ! /[(i-1) !(n-i) !] \int_0^1 Y_{[i]}\left[F\left(y_{[i]}\right)\right]^{(i-1)}\left[1-F\left(y_{[i]}\right)\right]^{(n-i)} d F\left(y_{[i]}\right)$$

，其中$\mathrm{f}(\mathrm{y})$表示正在考虑的PDF, $\mathrm{F}(\mathrm{y})$表示相关的累积分布函数(cdf)， $\mathrm{n}$表示正在调查的数据集的大小。因为这个方程的数值解可能很困难，所以经常使用近似$E\left(Y_{[i]}\right)=F^{-1}[(i-c) /(n-2 c-1)]$，其中$F^{-1}$表示逆$c d f$和$c$一个常数$(0 \leq c \leq 1)$。设置$c=0.5$(参见Kimball(1960))的结果是
$$E\left(Y_{[i]}\right)=F^{-1}[(i-0.5) / n]$$
，这是这里使用的近似。Mathematica将用于评估$E\left(Y_{[i]}\right)$，创建产生的概率图，协助评估线性和确定参数估计。
Mathematica的Quantile函数用于查找特定pdf的$E\left(Y_{[i]}\right)^{\prime}$ s，并创建$Y_{[i]}$与$E\left(Y_{[i]}\right)$的关系图。如果结果图被认为是线性的，那么用来确定$E\left(Y_{[i]}\right)^{\prime}$ s的pdf可以用来描述数据的随机结构。假设图被认为是线性的，可以从图中确定未知参数的估计。

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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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师