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# 统计代写|非参数统计代写Nonparametric Statistics代考|ST505 RANDOM SAMPLE

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## 统计代写|非参数统计代写Nonparametric Statistics代考|RANDOM SAMPLE

Much of statistical inference is based on the key idea of a random sample. A random sample is a sample of observations taken from a population so that each observation from the population has an equal chance of being selected in the sample. Stated differently, the selection of each element should be governed purely by chance with no predictability. Put in a more mathematical way, a random sample is a set or a collection of random variables that are independent and identically distributed, denoted as i.i.d.Another important concept is the moment of a random variable, which may be used as a descriptor of the location, the variance and the shape of its probability distribution. The moments can be used to identify a distribution; the reader can consult a standard mathematical statistics book for more details. The $r$ th raw moment is given by $E\left(X^{r}\right)$ for $r=1,2, \ldots$, so that the first raw moment, for $r=1$, is $E(X)$, the mean of the distribution, that is, the expected value, which is a measure of location or the central tendency of a distribution. The mean is typically denoted as $\mu$. Depending on the range of the distribution, the mean $\mu$ can take on any value over the real line, which is illustrated in Figure $1.3$ for a continuous symmetric distribution. Indeed, it can be shown that for any symmetric distribution, continuous or discrete, the point of symmetry equals the mean of the distribution.

## 统计代写|非参数统计代写Nonparametric Statistics代考|STATISTICAL INFERENCE

Statistical inference means drawing conclusions about a population based on data from a random sample that is a subset of the population. Typically, population parameters are unknown and, consequently, sample statistics (also referred to as point estimators) are used to obtain estimates of these unknown population parameters. Table $1.3$ lists some frequently encountered population parameters in Column (a) along with the corresponding point estimators in Column (b). The absolute difference (or the ratio) between the population parameter and the point estimator is referred to as the sampling error, and this is given in Column (c) of Table 1.3. Typically, for a location parameter, the sampling error involves the difference, whereas for a scale parameter, the sampling error is expressed as a ratio.

It may be noted that one important parameter of interest, not shown in Table $1.3$, is the population median, which is also the 50 th percentile of the distribution. Thus, $50 \%$ of the cumulative probability must be at or below the median. While the median can be defined uniquely for most continuous distributions, that is not the case for the discrete distributions, which has jumps in its cdf (see Figure 1.1), and one needs to define the median (a percentile) so that it is unique. We mentioned this point before Table $1.1$, and we discuss this later in Chapter 2. The population median is estimated by the sample median and the sample median is defined as the observation in the middle (of the sample ordered from the lowest to the highest) when the sample size is odd and as the average of the two middle observations when the sample size is even. The sample median is generally the preferred estimator of the center (location) of a skewed distribution form a robustness point of view. The median plays an important role in SPC and will be discussed further later in the book.

## 统计代写|非参数统计代写NONPARAMETRIC STATISTICS代 考|STATISTICAL INFERENCE

ofthesampleordered fromthelowesttothehighest当样本量为奇数时，当样本量为偶数时，作为两个中间观测值的平均值。样本中位数通常是中心的首选估计 量location偏态分布形成稳健性的观点。中位数在 SPC 中起着重要作用，本书后面将进一步讨论。

## 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。