## 统计代写|随机过程代写stochastic process代考|MTH3016

statistics-lab™ 为您的留学生涯保驾护航 在代写随机过程stochastic process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过程stochastic process代写方面经验极为丰富，各种代写随机过程stochastic process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|随机过程代写stochastic process代考|Hexagonal Lattice, Nearest Neighbors

Here I dive into the details of the processes discussed in Section 1.5.3. I also discuss Figure 2. The source code to produce Figure 2 is discussed in Sections $6.4$ (nearest neighbor graph) and $6.7$ (visualizations). Some elements of graph theory are discussed here, as well as visualization techniques.

Surprisingly, it is possible to produce a point process with a regular hexagonal lattice space using simple operations on a small number $(m=4)$ of square lattices: superimposition, stretching, and shifting. A stretched lattice is a square lattice turned into a rectangular lattice, by applying a multiplication factor to the $\mathrm{X}$ and/or Y coordinates. A shifted lattice is a lattice where the grid points have been shifted via a translation.

Each point of the process almost surely (with probability one) has exactly one nearest neighbor. However, when the scaling factor $s$ is zero, this is no longer true. On the left plot in Figure 2, each point (also called vertex when $s=0$ ) has exactly 3 nearest neighbors. This causes some challenges when plotting the case $s=0$. The case $s>0$ is easier to plot, using arrows pointing from any point to its unique nearest neighbor. I produced the arrows in question with the arrow function in R, see source code in Section $6.7$, and online documentation here. $\mathrm{A}$ bidirectional arrow between points $\mathrm{A}$ and $\mathrm{B}$ means that $\mathrm{B}$ is a nearest neighbor of $\mathrm{A}$, and $\mathrm{A}$ is a nearest neighbor of B. All arrows on the left plot in Figure 2 are bidirectional. Boundary effects are easily noticeable, as some arrows point to nearest neighbors outside the window. Four colors are used for the points, corresponding to the 4 shifted stretched Poisson-binomial processes used to generate the hexagon-based process. The color indicates which of these 4 process, a point is attached to.

The source code in Section $6.4$ handles points with multiple nearest neighbors. It produces a list of all points with their nearest neighbors, using a hash table. A point with 3 nearest neighbors has 3 entries in that list: one for each nearest neighbor. A group of points that are all connected by arrows, is called a connected component [Wiki]. A path from a point of a connected component to another point of the same connected component, following arrows while ignoring their direction, is called a path in graph theory.

In my definition of connected component, the direction of the arrow does not matter: the underlying graph is considered undirected [Wiki]. An interesting problem is to study the size distribution, that is, the number of points per connected component, especially for standard Poisson processes. See Exercise 20. In graph theory, a point is called a vertex or node, and an arrow is called an edge. More about nearest neighbors is discussed in Exercises 18 and 19.

Finally, if you look at Figure 2, the left plot seems to have more points than the right plot. But they actually have roughly the same number of points. The plot on the right seems to be more sparse, because there are large areas with no points. But to compensate, there are areas where several points are in close proximity.

## 统计代写|随机过程代写stochastic process代考|Modeling Cluster Systems in Two Dimensions

There are various ways to create points scattered around a center. When multiple centers are involved, we get a cluster structure. The point process consisting of the centers is called the parent process, while the point distribution around each center, is called the child process. So we are dealing with a two-layer, or hierarchical structure, referred to as a cluster point process. Besides clustering, many other types of point process operations [Wiki] are possible when combining two processes, such as thinning or superimposition. Typical examples of cluster point processes include Neyma-Scott (see here) and Matérn (see here).

Useful references include Baddeley’s textbook “Spatial Point Processes and their Applications” [4] available online here, Sigman’s course material (Columbia University) on one-dimensional renewal processes for beginners, entitled “Notes on the Poisson Process” [71], available online here, Last and Kenrose’s book “Lectures on the Poisson Process” [52], and Cressie’s comprehensive 900-page book “Statistics for Spatial Data” [16]. Cluster point processes are part of a larger field known as spatial statistics, encompassing other techniques such as geostatistics, kriging and tessellations. For lattice-based processes known as perturbed lattice point processes, more closely related to the theme of this textbook (lattice processes), and also more recent with applications to cellular networks, see the following references:

• “On Comparison of Clustering Properties of Point Processes” [12]. Online PDF here.
• “Clustering and percolation of point processes” [11]. Online version here.
• “Clustering comparison of point processes, applications to random geometric models” [13]. Online version here.
• “Stochastic Geometry-Based Tools for Spatial Modeling and Planning of Future Cellular Networks” [51]. Online version here.
• “Hyperuniform and rigid stable matchings” [54]. Online PDF here. Short presentation available here.
• “Rigidity and tolerance for perturbed lattices” [68]. Online version here.
• “Cluster analysis of spatial point patterns: posterior distribution of parents inferred from offspring” [66].
• “Recovering the lattice from its random perturbations” [79]. Online version here.
• “Geometry and Topology of the Boolean Model on a Stationary Point Processes” [81]. Online version here.
• “On distances between point patterns and their applications” [56]. Online version here.
More general references include two comprehensive volumes on point process theory by Daley and Vere-Jones [20, 21], a chapter by Johnson [45] (available online here or here), books by Møller and Waagepetersen, focusing on statistical inference for spatial processes [60, 61], and “Point Pattern Analysis: Nearest Neighbor Statistics” by Anselin [3] focusing on point inhibition/aggregation metrics, available here. See also [58] by Møller, available online here, and “Limit Theorems for Network Dependent Random Variables” [48], available online here.

# 随机过程代考

## 统计代写|随机过程代写stochastic process代考|Modeling Cluster Systems in Two Dimensions

• 《论点过程的聚类特性比较》[12]。此处为在线 PDF。
• “点过程的聚类和渗透”[11]。在线版本在这里。
• “点过程的聚类比较，在随机几何模型中的应用”[13]。在线版本在这里。
• “用于未来蜂窝网络空间建模和规划的基于随机几何的工具”[51]。在线版本在这里。
• “超均匀和刚性稳定匹配”[54]。此处为在线 PDF。此处提供简短演示。
• “扰动格子的刚度和容忍度”[68]。在线版本在这里。
• “空间点模式的聚类分析：从后代推断出父母的后验分布”[66]。
• “从随机扰动中恢复晶格”[79]。在线版本在这里。
• “驻点过程布尔模型的几何和拓扑”[81]。在线版本在这里。
• “关于点模式之间的距离及其应用”[56]。在线版本在这里。
更一般的参考资料包括 Daley 和 Vere-Jones [20, 21] 的两本关于点过程理论的综合性著作，Johnson [45] 的一章（可在此处或此处在线获取），Møller 和 Waagepetersen 的书籍，侧重于空间的统计推断过程 [60、61] 和 Anselin [3] 的“点模式分析：最近邻统计”重点关注点抑制/聚合指标，可在此处获取。另请参见 Møller 的 [58]，可在此处在线获取，以及“网络相关随机变量的极限定理”[48]，可在此处在线获取。

## 有限元方法代写

tatistics-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。

## 统计代写|随机过程代写stochastic process代考|MTH7090

statistics-lab™ 为您的留学生涯保驾护航 在代写随机过程stochastic process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过程stochastic process代写方面经验极为丰富，各种代写随机过程stochastic process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|随机过程代写stochastic process代考|Rotation, Stretching, Translation and Standardization

In two dimensions, rotating a Poisson-binomial process is equivalent to rotating its underlying lattice attached to the index space. Rotating the points has the same effect as rotating the lattice locations, because $F$ (the distribution attached to the points) belongs to a family of location-scale distributions [Wiki]. For instance, a $\pi / 4$ rotation will turn the square lattice into a centered-square lattice [Wiki], but it won’t change the main properties of the point process. Both processes, the original one and the rotated one, may be indistinguishable for all practical purposes unless the scaling factor $s$ is small, creating model identifiability [Wiki] issues. For instance, the theoretical correlation between the point coordinates $\left(X_h, Y_k\right)$ or the underlying lattice point coordinates $(h / \lambda, k / \lambda)$, measured on all points, remains equal to zero after rotation, because the number of points is infinite (this may not be the case if you observe points through a small window, because of boundary effects). Thus, a Poisson-binomial process has a point distribution invariant under rotations, on a macro-scale. This property is called anisotropy [Wiki]. On a micro-scale, a few changes occur though: for instance the twodimensional version of Theorem $4.1$ no longer applies, and the distance between the projection of two neighbor points on the $\mathrm{X}$ or $\mathrm{Y}$ axis, shrinks after the rotation.

Applying a translation to the points of the process, or to the underlying lattice points, results in a shifted point process. It becomes interesting when multiple shifted processes, with different translation vectors, are combined together as in Section 1.5.3. Theorem $4.1$ may not apply to the shifted process, though it can easily be adapted to handle this situation. One of the problems is to retrieve the underlying lattice space of the shifted process. This is useful for model fitting purposes, as it is easier to compare two processes once they have been standardized (after removing translations and rescaling). Estimation techniques to identify the shift are discussed in Section 3.4.

By a standardized Poisson-binomial point process, I mean one in its canonical form, with intensity $\lambda=1$, scaling factor $s=1$, and free of shifts or rotations. Once two processes are standardized, it is easier to compare them, assess if they are Poisson-binomial, or perform various machine learning procedures on observed data, such as testing, computing confidence intervals, cross-validation, or model fitting. In some way, this is similar to transforming and detrending time series to make them more amenable to statistical inference. There is also some analogy between the period or quasi-period of a time series, and the inverse of the intensity $\lambda$ of a Poisson-binomial process: in fact, $1 / \lambda$ is the fixed increment between the underlying lattice points in the lattice space, and can be viewed as the period of the process.

Finally, a two dimensional process is said to be stretched if a different intensity is used for each coordinate for all the points of the process. It turns the underlying square lattice space into a rectangular lattice, and the homogeneous process into a non-homogeneous one, because the intensity varies locally. Observed data points can be standardized using the Mahalanobis transformation [Wiki], to remove stretching (so that variances are identical for both coordinates) and to decorrelate the two coordinates, when correlation is present.

## 统计代写|随机过程代写stochastic process代考|Superimposition and Mixing

Here we are working with two-dimensional processes. When the points of $m$ independent point processes with same distribution $F$ and same index space $\mathbb{Z}^2$ are bundled together, we say that the processes are superimposed. These processes are no longer Poisson-binomial, see Exercise 14. Indeed, if the scaling factor $s$ is small and $m>1$ is not too small, they exhibit clustering around each lattice location in the lattice space. Also, the intensities or scaling factors of each individual point process may be different, and the resulting combined process may not be homogeneous. Superimposed point processes also called interlaced processes.
A mixture of $m$ point processes, denoted as $M$, is defined as follows:

• We have $m$ independent point processes $M_1, \ldots, M_m$ with same distribution $F$ and same index space $\mathbb{Z}^2$,
• The intensity and scaling factor attached to $M_i$ are denoted respectively as $\lambda_i$ and $s_i(i=1, \ldots, m)$,
• The points of $M_i(i=1, \ldots, m)$ are denoted as $\left(X_{i h}, Y_{i k}\right)$; the index space consists of the $(h, k)$ ‘s,
• The point $\left(X_h, Y_k\right)$ of the mixture process $M$ is equal to $\left(X_{i h}, Y_{i k}\right)$ with probability $\pi_i>0, i=1, \ldots, m$.
While mixing or superimposing Poisson-binomial processes seem like the same operation, which is true for stationary Poisson processes, in the case of Poisson-binomial processes, these are distinct operations resulting in significant differences when the scaling factors are very small (see Exercise 18). The difference is most striking when $s=0$. In particular, superimposed processes are less random than mixtures. This is due to the discrete nature of the underlying lattice space. However, with larger scaling factors, the behavior of mixed and superimposed processes tend to be similar.

Several of the concepts discussed in Section $1.5$ are illustrated in Figure 2, representing a realization of $m$ superimposed shifted stretched Poisson-binomial processes, called $m$-interlacing. For each individual process $M_i, i=1, \ldots, m$, the distribution attached to the point $\left(X_{i h}, X_{i k}\right)$ (with $h, k \in \mathbb{Z}$ ) is
$$P\left(X_{i h}<x, Y_{i k}<y\right)=F\left(\frac{x-\mu_i-h / \lambda}{s}\right) F\left(\frac{y-\mu_i^{\prime}-k / \lambda^{\prime}}{s}\right), \quad i=1, \ldots, m$$
This generalizes Formula (2). The parameters used for the model pictured in Figure 2 are:

• Number of superimposed processes: $m=4$; each one displayed with a different color,
• Color: red for $M_1$, blue for $M_2$, orange for $M_3$, black for $M_4$,
• scaling factor: $s=0$ (left plot) and $s=5$ (right plot),
• Intensity: $\lambda=1 / 3$ ( $\mathrm{X}$-axis) and $\lambda^{\prime}=\sqrt{3} / 3$ ( $\mathrm{Y}$-axis),
• Shift vector, $\mathrm{X}$-coordinate: $\mu_1=0, \mu_2=1 / 2, \mu_3=2, \mu_4=3 / 2$,
• Shift vector, Y-coordinate: $\mu_1^{\prime}=0, \mu_2^{\prime}=\sqrt{3} / 2, \mu_3^{\prime}=0, \mu_4^{\prime}=\sqrt{3} / 2$,
• $F$ distribution: standard centered logistic with zero mean and variance $\pi^2 / 3$.

# 随机过程代考

## 统计代写|随机过程代写stochastic process代考|Superimposition and Mixing

• 我们有 $m$ 独立点过程 $M_1, \ldots, M_m$ 具有相同的分布 $F$ 和相同的索引空间 $\mathbb{Z}^2$ ，
• 附加的强度和比例因子 $M_i$ 分别记为 $\lambda_i$ 和 $s_i(i=1, \ldots, m)$,
• 的要点 $M_i(i=1, \ldots, m)$ 表示为 $\left(X_{i h}, Y_{i k}\right)$ ；索引空间由 $(h, k)$ 的，
• 重点 $\left(X_h, Y_k\right)$ 混合过程 $M$ 等于 $\left(X_{i h}, Y_{i k}\right)$ 有概率 $\pi_i>0, i=1, \ldots, m$. 虽然混合或諿加泊松二项式过程看起来像是相同的操作，对于平稳泊松过程也是如此，但在泊松二 项式过程的情况下，这些是不同的操作，当缩放因子非常小时会导致显着差异 (参见练习 18). 当 $s=0$. 特别是，咺加过程的随机性低于混合过程。这是由于底层晶格空间的离散性质。然而，对 于较大的比例因子，混合过程和䝁加过程的行为往往相似。
本节中讨论的几个概念 $1.5$ 如图 2 所示，代表了一种实现 $m$ 呾加的偏移拉伸泊松二项式过程，称为 $m$ – 交 错。对于每个单独的过程 $M_i, i=1, \ldots, m$, 分布附加到点 $\left(X_{i h}, X_{i k}\right.$ ) (和 $h, k \in \mathbb{Z}$ ) 是
$$P\left(X_{i h}<x, Y_{i k}<y\right)=F\left(\frac{x-\mu_i-h / \lambda}{s}\right) F\left(\frac{y-\mu_i^{\prime}-k / \lambda^{\prime}}{s}\right), \quad i=1, \ldots, m$$
这推广了公式 (2)。用于图 2 中所示模型的参数是:
• 㠬加进程数： $m=4$; 每一个都以不同的颜色显示，
• 颜色: 红色为 $M_1$ ，蓝色为 $M_2$ ，橙色为 $M_3$ ，黑色为 $M_4$ ，
• 比例因子: $s=0$ (左图) 和 $s=5$ (右图),
• 强度: $\lambda=1 / 3$ ( $\mathrm{X}$-轴) 和 $\lambda^{\prime}=\sqrt{3} / 3$ (Y-轴)，
• 移位向量， $\mathrm{X}$-协调: $\mu_1=0, \mu_2=1 / 2, \mu_3=2, \mu_4=3 / 2$,
• 移位向量， Y坐标: $\mu_1^{\prime}=0, \mu_2^{\prime}=\sqrt{3} / 2, \mu_3^{\prime}=0, \mu_4^{\prime}=\sqrt{3} / 2$,
• $F$ 分布: 均值和方差为零的标准中心逻辑 $\pi^2 / 3$.

## 有限元方法代写

tatistics-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。

## 统计代写|随机过程代写stochastic process代考|STAT3021

statistics-lab™ 为您的留学生涯保驾护航 在代写随机过程stochastic process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过程stochastic process代写方面经验极为丰富，各种代写随机过程stochastic process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|随机过程代写stochastic process代考|Point Count and Interarrival Times

An immediate result is that $F_s(x-k / \lambda)$ is centered at $k / \lambda$. Also, if $s=0$, then $X_k=k / \lambda$. If $s$ is very small, $X_k$ is very close to $k / \lambda$ most of the time. But when $s$ is large, the points $X_k$ ‘s are no longer ordered, and the larger $s$, the more randomly they are permutated (or shuffled, or mixed) on the real line.
Let $B=[a, b]$ be an interval on the real line, with $a2$. This is due to the combinatorial nature of the Poisson-binomial distribution. But you can easily obtain approximated values using simulations.

Another fundamental, real-valued random variable, denoted as $T$ or $T(\lambda, s)$, is the interarrival times between two successive points of the process, once the points are ordered on the real line. In two dimensions, it is replaced by the distance between a point of the process, and its nearest neighbor. Thus it satisfies (see Section $4.2$ ) the following identity:
$$P(T>y)=P[N(B)=0],$$
with $\left.B=] X_0, X_0+y\right]$, assuming it is measured at $X_0$ (the point of the process corresponding to $k=0$ ). See Formula (38) for the distribution of $T$. In practice, this intractable exact formula is not used; instead it is approximated via simulations. Also, the point $X_0$ is not known, since the $X_k$ ‘s are in random order, and retrieving $k$ knowing $X_k$ is usually not possible. The indices (the $k$ ‘s) are hidden. However, see Section $4.7$. The fundamental question is whether using $X_0$ or any $X_k$ (say $X_5$ ), matters for the definition of $T$. This is discussed in Section $1.4$ and illustrated in Table 4.

## 统计代写|随机过程代写stochastic process代考|Limiting Distributions, Speed of Convergence

I prove in Theorem $4.5$ that Poisson-binomial processes converge to ordinary Poisson processes. In this section, I illustrate the rate of convergence, both for the interarrival times and the point count in one dimension.

In Figure 1 , we used $\lambda=1$ and $B=[-0.75,0.75] ; \mu(B)=1.5$ is the length of $B$. The limiting values (combined with those of Table 3), as $s \rightarrow \infty$, are in agreement with $N(B)$ ‘s moments converging to those of a Poisson distribution of expectation $\lambda \mu(B)$, and $T$ ‘s moments to those of an exponential distribution of expectation $1 / \lambda$. In particular, it shows that $P[N(B)=0] \rightarrow \exp [-\lambda \mu(B)]$ and $E\left[T^2\right] \rightarrow 2 / \lambda$ as $s \rightarrow \infty$. These limiting distributions are features unique to stationary Poisson processes of intensity $\lambda$.

Figure 1 illustrates the speed of convergence of the Poisson-binomial process to the stationarity Poisson process of intensity $\lambda$, as $s \rightarrow \infty$. Further confirmation is provided by Table 3 , and formally established by Theorem 4.5. Of course, when testing data, more than a few statistics are needed to determine whether you are dealing with a Poisson process or not. For a full test, compare the empirical moment generating function (the estimated $\mathrm{E}\left[T^r\right]^{\prime}$ s say for all $r \in[0,3]$ ) or the empirical distribution of the interarrival times, with its theoretical limit (possibly obtained via simulations) corresponding to a Poisson process of intensity $\lambda$. The parameter $\lambda$ can be estimated based on the data. See details in Section 3.

In Figure 1, the values of $\mathrm{E}\left[T^2\right]$ are more volatile than those of $P[N(B)=0]$ because they were estimated via simulations; to the contrary, $P[N(B)=0]$ was computed using the exact Formula (6), though truncated to 20,000 terms. The choice of a Cauchy or logistic distribution for $F$ makes almost no difference. But a uniform $F$ provides noticeably slower, more bumpy convergence. The Poisson approximation is already quite good with $s=10$, and only improves as $s$ increases. Note that in our example, $N(B)>0$ if $s=0$. This is because $X_k=k$ if $s=0$; in particular, $X_0=0 \in B=[-0.75,0.75]$. Indeed $N(B)>0$ for all small enough $s$, and this effect is more pronounced (visible to the naked eye on the left plot, blue curve in Figure 1 ) if $F$ is uniform. Likewise, $E\left[T^2\right]=1$ if $s=0$, as $T(\lambda, s)=\lambda$ if $s=0$, and here $\lambda=1$.

The results discussed here in one dimension easily generalize to higher dimensions. In that case $B$ is a domain such as a circle or square, and $T$ is the distance between a point of the process, and its nearest neighbor. The limit. Poisson process is stationary with intensity $\lambda^d$, where $d$ is the dimension.

# 随机过程代考

## 统计代写|随机过程代写stochastic process代考|Point Count and Interarrival Times

$$P(T>y)=P[N(B)=0],$$

## 有限元方法代写

tatistics-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。

## 会计代写|财务会计代写Financial Accounting代考|TACC203

statistics-lab™ 为您的留学生涯保驾护航 在代写财务会计Financial Accounting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。我们的专家在代写财务会计Financial Accounting代写方面经验极为丰富，各种代写财务会计Financial Accounting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

## 会计代写|财务会计代写Financial Accounting代考|International influences

As noted at the beginning of this chapter, many nations have contributed to the development of accounting. In the case of some countries, ideas have been transferred wholesale from another country, such as the following:

Several African countries that are members of the (British) Commonwealth have accounting systems closely based on that of the British Companies Acts of 1929 or 1948.

• The French plan comptable général was introduced into France in the 1940s, based closely on a German precedent, and later into several former French colonies in Africa.
• The Japanese accounting system consists largely of a commercial code borrowed from Germany in the late nineteenth century, overlaid with US-style securities laws imposed in the late 1940 s.

By the end of the twentieth century, international influences had begun to affect accounting in all countries, sometimes overwhelmingly. The globalisation of markets had led to an increased need for internationally comparable accounting information. Where several large multinational companies are based in comparatively small countries (e.g. Hong Kong, Singapore, the Netherlands and Sweden), international influences are likely to be particularly great.

Many large European companies responded to internationalisation by volunteering to use one of two sets of internationally recognised rules: the United States’ generally accepted accounting principles (GAAP) and the international standards of the IASB. In general – in Europe at least – this usage has been mostly restricted to the consolidated financial statements prepared for groups headed by listed companies. As noted in Chapter 4 , there are EU requirements in this area from 2005.

Another effect has been that national rule-makers have been trying to reduce differences between their national rules and the above international norms. At the extreme, certain countries (e.g. South Africa) have directly adopted IFRS as part of their national rules. These issues were noted in Chapter 4 and are taken up again in Section 5.5.

## 会计代写|财务会计代写Financial Accounting代考|Introduction to harmonisation

So far, this chapter has made it clear that there are major differences in the financial reporting practices of companies in different countries. This leads to great complications for those preparing, consolidating, auditing and interpreting published financial statements. Since the preparation of internal financial information often overlaps with the preparation of published information, the complications spread into management accounting. To combat these problems, several organisations throughout the world are involved in attempts to harmonise or standardise accounting.
‘Harmonisation’ is a process of increasing the compatibility of accounting practices by setting bounds to their degree of variation. ‘Standardisation’ appears to imply the imposition of a more rigid and narrow set of rules. However, within accounting these two words have almost become technical terms, so one cannot rely upon the normal difference in their meanings. Harmonisation is a word that tends to be associated with the supranational legislation promulgated in the European Union, while standardisation is a word often associated with the International Accounting Standards Board. In practice, the words are often used interchangeably. Convergence is a newer word, in this context, and means the gradual aligning of IFRS and US GA $A P$, followed by other jurisdictions aligning with the result of that.

It is necessary to distinguish between de jure harmonisation (that of rules, standards, etc.) and de facto harmonisation (that of corporate financial reporting practices). For any particular topic or set of countries, it is possible to have one of these two forms of harmonisation without the other. For example, countries or companies may ignore the harmonised rules of standard setters or even law-makers. By contrast, in the $1980 \mathrm{~s}$, market forces persuaded many listed companies in France and Switzerland to volunteer to produce English-language financial reports that approximately followed Anglo-American practice. Even among a large set of companies using IFRS (i.e. with de jure identity), there may be differences in policy choice because IFRS allows many areas of choice (i.e. de facto variety). However, there might then be gradual harmonisation within an industry as companies seek to be more comparable.

The EU achieves its harmonising objectives mainly through Directives (which must be incorporated into the laws of member states) and Regulations (which have direct effect). In the 1970 s and 1980 s attention was given to harmonising national laws through Directives (see Sections 5.4.2 and 5.4.3 below). During the 1990 s, the EU began to take more notice of international standards, leading to a Regulation of 2002 requiring IFRS for the consolidated statements of listed companies (see Section 5.4.4).

# 财务会计代考

## 会计代写|财务会计代写Financial Accounting代考|International influences

• 法国 plan comptable général 在 1940 年代被引入法国，严格遵循德国的先例，后来又被引入非洲的几个前法国殖民地。
• 日本的会计制度主要由 19 世纪末从德国借来的商业法典组成，外加 1940 年代末实施的美国式证券法。

## 会计代写|财务会计代写Financial Accounting代考|Introduction to harmonisation

“协调”是通过设定差异程度的界限来增加会计实践的兼容性的过程。“标准化”似乎意味着强加一套更加严格和狭隘的规则。然而，在会计中，这两个词几乎已成为专业术语，因此不能依赖它们在含义上的正常差异。协调这个词往往与欧盟颁布的超国家立法相关联，而标准化这个词通常与国际会计准则委员会相关联。在实践中，这些词经常互换使用。趋同是一个较新的词，在这种情况下，意味着 IFRS 和 US GA 的逐渐统一一个P，其次是与该结果一致的其他司法管辖区。

## 有限元方法代写

tatistics-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。

## 会计代写|财务会计代写Financial Accounting代考|MGB001

statistics-lab™ 为您的留学生涯保驾护航 在代写财务会计Financial Accounting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。我们的专家在代写财务会计Financial Accounting代写方面经验极为丰富，各种代写财务会计Financial Accounting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

## 会计代写|财务会计代写Financial Accounting代考|An updated classification

The above classifications were drawn up before the EU harmonisation programme and before extensive globalisation of capital markets. The fall of communism also means that many more countries, such as China and Russia, have financial reporting systems that could be added to the 1983 classification. Some countries, such as Sweden have moved to the left of the chart since the early 1980s, as has Norway, which was not in the chart.

A further complication is that, particularly from the middle 1990 s and in certain countries, large companies chose to follow internationally recognised practices rather than domestic practices. For example, by 2000 most of the 50 largest German companies were using US GAAP or IFRS for their group accounting statements. In a sense, then, several ‘systems’ were being used in Germany. In 1998, Nobes published a revised classification to try to take account of some of these problems. An adapted version of this is shown as Figure 5.2. To repeat a point from earlier, the fact that the United Kingdom and the United States are both on the left of Table $5.3$ and Figure $5.2$ does not imply that they are the same. For example, their regulatory systems are noticeably different. However, when compared to French or German accounting practices, UK and US practices look relatively similar.

The use of two systems within a country has increased greatly since IFRS was required in the EU for the consolidated reporting of listed companies. This is a major example of the fact that practices vary between companies within a country. It is also clear that different national versions of IFRS practice have emerged. In 2011, Nobes published a paper which used a survey of IFRS policy choices to show that the classification of 1983 was largely still in place after nearly 30 years of attempts at harmonisation in Europe.

## 会计代写|财务会计代写Financial Accounting代考|Providers of finance

In some countries, a major source of corporate finance for two centuries has been the share capital and loan capital provided by large numbers of private investors. This has been the predominant mode of raising finance for large companies in the Netherlands, the United States and the United Kingdom. Although it is increasingly the case that shares in these countries are held by institutional investors, such as pension funds, rather than by individual shareholders, this still contrasts with state, bank or family holdings (see below). Indeed, the increased importance of institutional investors is perhaps a reinforcement for the following hypothesis: ‘In countries with a widespread ownership of companies by shareholders who do not have access to internal information, there will be a pressure for disclosure, audit and decision-useful information’. Institutional investors hold larger blocks of shares and may be better organised than private shareholders, so they should increase this pressure.

By contrast, in France and Italy, capital provided by the state or by banks is very significant, as are family businesses. In Germany, the banks, in particular, are important owners of shares in companies as well as providers of debt finance. A majority of shares in some German public companies are owned directly by banks or controlled through proxies by them. In such countries the banks or the state will, in many cases, nominate directors and thus be able to obtain non-public information and to affect decisions. If many companies in continental countries are dominated by banks, governments or families, the need for published information is much smaller because of this access to private information. This also applies to the need for audit, because this is designed to check up on the managers in cases where the owners are ‘outsiders’.

Evidence of the two-way characterisation of countries may be found by looking at their numbers of listed companies. Table $5.4$ shows the numbers, in late 2018, of domestic listed companies on selected stock exchanges. Table $5.5$ shows figures for four major countries in 2012, putting the size of the equity market in the context of the size of the economy and the number of domestic listed companies in the context of the population. The comparison between the United Kingdom and the United States (with large equity markets) and Germany and Italy (with much smaller equity markets) is instructive.

# 财务会计代考

## 有限元方法代写

tatistics-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。

## 会计代写|财务会计代写Financial Accounting代考|FNS50217

statistics-lab™ 为您的留学生涯保驾护航 在代写财务会计Financial Accounting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。我们的专家在代写财务会计Financial Accounting代写方面经验极为丰富，各种代写财务会计Financial Accounting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

## 会计代写|财务会计代写Financial Accounting代考|Introduction: the international nature

Different countries have contributed to the development of accounting over the centuries. When archaeologists uncover ancient remains in the Middle East, almost anything with writing or numbers on it is a form of accounting: expenses of wars, feasts or constructions; or lists of taxes due or paid. It is now fairly well documented that the origins of written numbers and written words are closely associated with the need to keep account and to render account.

The Romans developed sophisticated forms of single-entry accounting from which, for example, farm profits could be calculated. Later, India and the Arab world had sophisticated accounting, but it is probably in northern Italy in the thirteenth century that the double-entry system was invented, driven by the increasing complexity of business. Later still, in seventeenth-century Holland, the existence of a wealthy merchant class and the need for large investment for major projects led to public subscription of share capital. Next, the growing separation of ownership from management raised the need for audits in nineteenth-century Britain. Many European countries have contributed to the development of accounting: France led in legal control over accounting; Scotland pioneered the accountancy profession; Germany gave us standardised formats for financial statements.

From the late nineteenth century onwards, the United States has given us consolidation of financial statements (see Chapter 14), management accounting, capitalisation of leases (see Chapter 9) and deferred tax accounting (see Chapter 12). The United Kingdom contributed the ‘true and fair view’ (see Section 5.4), which has been rounded out with the US ‘substance over form’. In the late twentieth century, Japan contributed greatly to managerial accounting and control.

The common feature of all these international influences on accounting is that commercial developments led to accounting advances. Not surprisingly, leading commercial nations in any period are the innovators in accounting. However, although international influences and similarities are clear, there are also great international differences, particularly within Europe. An indication of the scale of international difference can be seen in those cases where companies publish two sets of accounting figures based on different rules. Comparisons of accounting under domestic rules with that under US rules were commonly published until 2006 by foreign companies that were listed on US stock exchanges. Table $5.1$ shows some interesting examples for earnings. Daimler-Benz was the first German company to provide this data, in 1993 . The large differences (and the variation from year to year) between German and US profit figures were a surprise to many accountants and users of financial statements.

## 会计代写|财务会计代写Financial Accounting代考|Nobes’ classification

It would be possible to criticise the classifications discussed above for:
(a) lack of precision in the definition of what is to be classified;
(b) lack of a model with which to compare the statistical results;
(c) lack of hierarchy that would add more subtlety to the portrayal of the size of differences between countries;
(d) lack of judgement in the choice of ‘important’ discriminating features.
Can these problems be remedied? One of the authors of this book attempted to solve them in the following ways (see Nobes, 1983). The scope of the exercise was defined as the classification of some Western countries by the financial reporting practices of their listed companies and it was carried out in the early 1980s. The reporting practices were those concerned with measurement and valuation. It is listed companies whose financial statements are generally available and whose practices can most easily be discovered. It is the international differences in reporting between such companies that are of main interest to shareholders, creditors, auditing firms, taxation authorities, management and harmonising agencies. Measurement and valuation practices were chosen because these determine the size of the figures for profit, capital, total assets, liquidity and so on.

Nobes (1983) suggested that there were two main types of financial reporting ‘system’ in Europe at the time: the micro/professional and the macro/uniform. The first of these involved accountants in individual companies striving to present tair information to outside users, without detailed constraint of law or tax rules but with standards written by accountants. The macro/uniform type had accounting mainly as a servant of the state, particularly for taxation purposes.

The micro/professional side contained the Netherlands, the United Kingdom, Ireland, Denmark, the United States, Australla, Canada, New Zealand and South Africa. The Netherlands had (and has) fewer rules than the other countries, and another distinguishing feature is that the influence of microeconomic theory led to the use of replacement cost information to varying degrees. Denmark rearranged its accounting system after the Second World War and it now looks somewhat like the United Kingdom’s or the United States’.

The macro/uniform side contained all other sample European countries and Japan. However, they were divided into subgroups. For example, accounting plans were (and are) the predominant source of detailed rules in France, Belgium, Spain and Greece. In Germany the commercial code was (and is) the major authority and there was (and is) much stricter observance of historical cost values. In Sweden, the predominant influence seems to have been the government as economic planner and tax collector.

Table $5.3$ summarises some of the typical differences between countries on a two-group basis. A number of the ‘specific accounting features’ are examined in Part 2.

# 财务会计代考

## 会计代写|财务会计代写Financial Accounting代考|Nobes’ classification

(a) 对要分类的内容的定义不够精确；
(b) 缺乏用于比较统计结果的模型；
(c) 缺乏等级制度，这会使对国家间差异规模的描述更加微妙；
(d) 在选择“重要”区别特征时缺乏判断力。

Nobes (1983) 建议当时欧洲有两种主要类型的财务报告“系统”：微观/专业和宏观/统一。其中第一个涉及个别公司的会计师，他们努力向外部用户提供公平信息，不受法律或税收规则的详细限制，但遵循会计师编写的标准。宏观/统一类型的会计主要作为国家的仆人，特别是出于税收目的。

## 有限元方法代写

tatistics-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。

## 经济代写|计量经济学代写Econometrics代考|ECON2271

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics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

## 经济代写|计量经济学代写Econometrics代考|Confidence Intervals

Estimation methods considered in Sect. $2.2$ give us a point estimate of a parameter, say $\mu$, and that is the best bet, given the data and the estimation method, of what $\mu$ might be. But it is always good policy to give the client an interval, rather than a point estimate, where with some degree of confidence, usually $95 \%$ confidence, we expect $\mu$ to lie. We have seen in Fig. $2.5$ that for a $N(0,1)$ random variable $z$, we have
$$\operatorname{Pr}\left[-z_{\alpha / 2} \leq z \leq z_{\alpha / 2}\right]=1-\alpha$$
and for $\alpha=5 \%$, this probability is $0.95$, giving the required $95 \%$ confidence. In fact, $z_{\alpha / 2}=1.96$ and
$$\operatorname{Pr}[-1.96 \leq z \leq 1.96]=0.95$$
This says that if we draw 100 random numbers from a $N(0,1)$ density, (using a normal random number generator) we expect 95 out of these 100 numbers to lie in the $[-1.96,1.96]$ interval. Now, let us get back to the problem of estimating $\mu$ from a random sample $x_1, \ldots, x_n$ drawn from a $N\left(\mu, \sigma^2\right)$ distribution. We found out that $\widehat{\mu}_{M L E}=\bar{x}$ and $\bar{x} \sim N\left(\mu, \sigma^2 / n\right)$. Hence, $z=(\bar{x}-\mu) /(\sigma / \sqrt{n})$ is $N(0,1)$. The point estimate for $\mu$ is $\bar{x}$ observed from the sample, and the $95 \%$ confidence interval for $\mu$ is obtained by replacing $z$ by its value in the above probability statement:
$$\operatorname{Pr}\left[-z_{\alpha / 2} \leq \frac{\bar{x}-\mu}{\sigma / \sqrt{n}} \leq z_{\alpha / 2}\right]=1-\alpha$$
Assuming $\sigma$ is known for the moment, one can rewrite this probability statement after some simple algebraic manipulations as
$$\operatorname{Pr}\left[\bar{x}-z_{\alpha / 2}(\sigma / \sqrt{n}) \leq \mu \leq \bar{x}+z_{\alpha / 2}(\sigma / \sqrt{n})\right]=1-\alpha$$
Note that this probability statement has random variables on both ends and the probability that these random variables sandwich the unknown parameter $\mu$ is $1-\alpha$. With the same confidence of drawing 100 random $N(0,1)$ numbers and finding 95 of them falling in the $(-1.96,1.96)$ range we are confident that if we drew a 100 samples and computed a $100 \bar{x}$ ‘s, and a 100 intervals $(\bar{x} \pm 1.96 \sigma / \sqrt{n}), \mu$ will lie in these intervals in 95 out of 100 times.

If $\sigma$ is not known, and is replaced by $s$, then Problem 12 shows that this is equivalent to dividing a $N(0,1)$ random variable by an independent $\chi_{n-1}^2$ random variable divided by its degrees of freedom, leading to a $t$-distribution with $(n-1)$ degrees of freedom. Hence, using the $t$-tables for $(n-1)$ degrees of freedom
$$\operatorname{Pr}\left[-t_{\alpha / 2 ; n-1} \leq t_{n-1} \leq t_{\alpha / 2 ; n-1}\right]=1-\alpha$$
and replacing $t_{n-1}$ by $(\bar{x}-\mu) /(s / \sqrt{n})$ one gets
$$\operatorname{Pr}\left[\bar{x}-t_{\alpha / 2 ; n-1}(s / \sqrt{n}) \leq \mu \leq \bar{x}+t_{\alpha / 2 ; n-1}(s / \sqrt{n})\right]=1-\alpha$$

## 经济代写|计量经济学代写Econometrics代考|Simple Linear Regression

In this chapter, we study extensively the estimation of a linear relationship between two variables, $Y_i$ and $X_i$, of the form:
$$Y_i=\alpha+\beta X_i+u_i \quad i=1,2, \ldots, n$$
where $Y_i$ denotes the $i$-th observation on the dependent variable $Y$ which could be consumption, investment, or output, and $X_i$ denotes the $i$-th observation on the independent variable $X$ which could be disposable income, the interest rate, or an input. These observations could be collected on firms or households at a given point in time, in which case we call the data a cross-section. Alternatively, these observations may be collected over time for a specific industry or country in which case we call the data a time-series. $n$ is the number of observations, which could be the number of firms or households in a cross-section, or the number of years if the observations are collected annually. $\alpha$ and $\beta$ are the intercept and slope of this simple linear relationship between $Y$ and $X$. They are assumed to be unknown parameters to be estimated from the data. A plot of the data, i.e., $Y$ versus $X$ would be very illustrative showing what type of relationship exists empirically between these two variables. For example, if $Y$ is consumption and $X$ is disposable income, then we would expect a positive relationship between these variables and the data may look like Fig. $3.1$ when plotted for a random sample of households. If $\alpha$ and $\beta$ were known, one could draw the straight line $(\alpha+\beta X)$ as shown in Fig. 3.1. It is clear that not all the observations $\left(X_i, Y_i\right)$ lie on the straight line $(\alpha+\beta X)$. In fact, Eq. (3.1) states that the difference between each $Y_i$ and the corresponding $\left(\alpha+\beta X_i\right)$ is due to a random error $u_i$. This error may be due to (i) the omission of relevant factors that could influence consumption, other than disposable income, like real wealth or varying tastes, or unforeseen events that induce households to consume more or less, (ii) measurement error, which could be the result of households not reporting their consumption or income accurately, or (iii) wrong choice of a linear relationship between consumption and income, when the true relationship may be nonlinear. These different causes of the error term will have different effects on the distribution of this error. In what follows, we consider only disturbances that satisfy some restrictive assumptions. In later chapters, we relax these assumptions to account for more general kinds of error terms.

## 经济代写|计量经济学代写Econometrics代考|Confidence Intervals

$$\operatorname{Pr}\left[-z_{\alpha / 2} \leq z \leq z_{\alpha / 2}\right]=1-\alpha$$

$$\operatorname{Pr}[-1.96 \leq z \leq 1.96]=0.95$$

$$\operatorname{Pr}\left[\bar{x}-z_{\alpha / 2}(\sigma / \sqrt{n}) \leq \mu \leq \bar{x}+z_{\alpha / 2}(\sigma / \sqrt{n})\right]=1-\alpha$$

$$\operatorname{Pr}\left[-t_{\alpha / 2 ; n-1} \leq t_{n-1} \leq t_{\alpha / 2 ; n-1}\right]=1-\alpha$$

$$\operatorname{Pr}\left[\bar{x}-t_{\alpha / 2 ; n-1}(s / \sqrt{n}) \leq \mu \leq \bar{x}+t_{\alpha / 2 ; n-1}(s / \sqrt{n})\right]=1-\alpha$$

## 经济代写|计量经济学代写Econometrics代考|Simple Linear Regression

$$Y_i=\alpha+\beta X_i+u_i \quad i=1,2, \ldots, n$$

## 有限元方法代写

tatistics-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。

## 经济代写|计量经济学代写Econometrics代考|BEA472

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics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

## 经济代写|计量经济学代写Econometrics代考|Comparing Biased and Unbiased Estimators

Suppose we are given two estimators $\widehat{\theta}_1$ and $\widehat{\theta}_2$ of $\theta$ where the first is unbiased and has a large variance and the second is biased but with a small variance. The question is which one of these two estimators is preferable? $\widehat{\theta}_1$ is unbiased whereas $\widehat{\theta}_2$ is biased. This means that if we repeat the sampling procedure many times, then we expect $\widehat{\theta}_1$ to be on the average correct, whereas $\widehat{\theta}_2$ would be on the average different from $\theta$. However, in real life, we observe only one sample. With a large variance for $\widehat{\theta}_1$, there is a great likelihood that the sample drawn could result in a $\widehat{\theta}_1$ far away from $\theta$. However, with a small variance for $\widehat{\theta}_2$, there is a better chance of getting a $\widehat{\theta}_2$ close to $\theta$. If our loss function is quadratic so that we are penalized when $\widehat{\theta}$ is different from $\theta$ by $L(\widehat{\theta}, \theta)=(\widehat{\theta}-\theta)^2$, then our risk is
\begin{aligned} R(\widehat{\theta}, \theta) &=E[L(\widehat{\theta}, \theta)]=E(\widehat{\theta}-\theta)^2=M S E(\widehat{\theta}) \ &=E[\widehat{\theta}-E(\widehat{\theta})+E(\widehat{\theta})-\theta]^2=\operatorname{var}(\widehat{\theta})+(\operatorname{Bias}(\widehat{\theta}))^2 . \end{aligned}
Minimizing the risk when the loss function is quadratic is equivalent to minimizing the Mean Square Error (MSE). From its definition the MSE shows the trade-off between bias and variance. MVU theory sets the bias equal to zero and minimizes $\operatorname{var}(\widehat{\theta})$. In other words, it minimizes the above risk function but only over $\widehat{\theta}$ ‘s that are unbiased. If we do not restrict ourselves to unbiased estimators of $\theta$, minimizing MSE may result in a biased estimator such as $\widehat{\theta}_2$ which beats $\widehat{\theta}_1$ because the gain from its smaller variance outweighs the loss from its small bias, see Fig. 2.2.

## 经济代写|计量经济学代写Econometrics代考|Hypothesis Testing

The best way to proceed is with an example.
Example 2.10. The Economics Departments instituted a new program to teach micro-principles. We would like to test the null hypothesis that $80 \%$ of economics undergraduate students will pass the micro-principles course versus the alternative hypothesis that only $50 \%$ will pass. We draw a random sample of size 20 from the large undergraduate micro-principles class, and as a simple rule we accept the null if $x$, the number of passing students is larger or equal to 13 , otherwise the alternative hypothesis will be accepted. Note that the distribution we are drawing from is Bernoulli with the probability of success $\theta$, and we have chosen only two states of the world $H_0 ; \theta_0=0.80$ and $H_1 ; \theta_1=0.5$. This situation is known as testing a simple hypothesis versus another simple hypothesis because the distribution is completely specified under the null $H_0$ or the alternative hypothesis $H_1$. One would expect $\left(E(x)=n \theta_0\right) 16$ students under $H_0$ and $\left(n \theta_1\right) 10$ students under $H_1$ to pass the micro-principles exams. It seems then logical to take $x \geq 13$ as the cutoff point distinguishing $H_0$ from $H_1$. No theoretical justification is given at this stage to this arbitrary choice except to say that it is the mid-point of $\lfloor 10,16]$. Figure $2.3$ shows that one can make two types of errors. The first is rejecting $H_0$ when in fact it is true; this is known as type I error and the probability of committing this error is denoted by $\alpha$. The second is accepting $H_0$ when it is false. This is known as type II error, and the corresponding probability is denoted by $\beta$. For this example
\begin{aligned} \alpha &=\operatorname{Pr}\left[\text { rejecting } H_0 / H_0 \text { is true }\right]=\operatorname{Pr}[x<13 / \theta=0.8] \ &=b(n=20 ; x=0 ; \theta=0.8)+. .+b(n=20 ; x=12 ; \theta=0.8) \ &=b(n=20 ; x=20 ; \theta=0.2)+. .+b(n=20 ; x=8 ; \theta=0.2) \ &=0+. .+0+0.0001+0.0005+0.0020+0.0074+0.0222=0.0322 \end{aligned}

where we have used the fact that $b(n ; x ; \theta)=b(n ; n-x ; 1-\theta)$ and $b(n ; x ; \theta)=$ $\left(\begin{array}{l}n \ x\end{array}\right) \theta^x(1-\theta)^{n-x}$ denotes the binomial distribution for $x=0,1, \ldots, n$, see Problem 4.
\begin{aligned} \beta &=\operatorname{Pr}\left[\text { accepting } H_0 / H_0 \text { is false }\right]=\operatorname{Pr}[x \geq 13 / \theta=0.5] \ &=b(n=20 ; x=13 ; \theta=0.5)+. .+b(n=20 ; x=20 ; \theta=0.5) \ &=0.0739+0.0370+0.0148+0.0046+0.0011+0.0002+0+0=0.1316 \end{aligned}

## 经济代写|计量经济学代写Econometrics代考|Comparing Biased and Unbiased Estimators

$$R(\hat{\theta}, \theta)=E[L(\hat{\theta}, \theta)]=E(\hat{\theta}-\theta)^2=M S E(\hat{\theta}) \quad=E[\hat{\theta}-E(\hat{\theta})+E(\hat{\theta})-\theta]^2=\operatorname{var}(\hat{\theta})+(\operatorname{Bias}$$

## 经济代写|计量经济学代写Econometrics代考|Hypothesis Testing

$\alpha=\operatorname{Pr}\left[\right.$ rejecting $H_0 / H_0$ is true $]=\operatorname{Pr}[x<13 / \theta=0.8] \quad=b(n=20 ; x=0 ; \theta=0.8)+\ldots+b(n$

$\beta=\operatorname{Pr}\left[\right.$ accepting $H_0 / H_0$ is false $]=\operatorname{Pr}[x \geq 13 / \theta=0.5] \quad=b(n=20 ; x=13 ; \theta=0.5)+\ldots+b$

## 有限元方法代写

tatistics-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。

## 经济代写|计量经济学代写Econometrics代考|ECON2300

statistics-lab™ 为您的留学生涯保驾护航 在代写计量经济学Econometrics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。我们的专家在代写计量经济学Econometrics代写方面经验极为丰富，各种代写计量经济学Econometrics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

## 经济代写|计量经济学代写Econometrics代考|Methods of Estimation

Consider a Normal distribution with mean $\mu$ and variance $\sigma^2$. This is the important “Gaussian” distribution which is symmetric and bell-shaped and completely determined by its measure of centrality, its mean $\mu$ and its measure of dispersion, its variance $\sigma^2 . \mu$ and $\sigma^2$ are called the population parameters. Draw a random sample $X_1, \ldots, X_n$ independent and identically distributed (IID) from this population. We usually estimate $\mu$ by $\widehat{\mu}=\bar{X}$ and $\sigma^2$ by
$$s^2=\sum_{i=1}^n\left(X_i-\bar{X}\right)^2 /(n-1)$$
For example, $\mu=$ mean income of a household in New York city. $\bar{X}=$ sample average of incomes of 1000 households randomly interviewed in New York city.
This estimator of $\mu$ could have been obtained by either of the following two methods of estimation:

(i) Method of Moments
Simply stated, this method of estimation uses the following rule: Keep equating population moments to their sample counterpart until you have estimated all the population parameters.
\begin{tabular}{l|l}
Population & Sample \
\hline & \
$E(X)=\mu$ & $\sum_{i=1}^n X_i / n=\bar{X}$ \
$E\left(X^2\right)=\mu^2+\sigma^2$ & $\sum_{i=1}^n X_i^2 / n$ \
$\vdots$ & $\vdots$ \
$E\left(X^r\right)$ & $\sum_{i=1}^n X_i^r / n$
\end{tabular}
The normal density is completely identified by $\mu$ and $\sigma^2$, hence only the first 2 equations are needed
$$\widehat{\mu}=\bar{X} \quad \text { and } \quad \widehat{\mu}^2+\widehat{\sigma}^2=\sum_{i=1}^n X_i^2 / n$$
Substituting the first equation in the second one obtains
$$\widehat{\sigma}^2=\sum_{i=1}^n X_i^2 / n-\bar{X}^2=\sum_{i=1}^n\left(X_i-\bar{X}\right)^2 / n$$

## 经济代写|计量经济学代写Econometrics代考|Properties of Estimators

(i) Unbiasedness
$\widehat{\mu}$ is said to be unbiased for $\mu$ if and only if $E(\widehat{\mu})=\mu$ For $\widehat{\mu}=\bar{X}$, we have $E(\bar{X})=\sum_{i-1}^n E\left(X_i\right) / n=\mu$ and $\bar{X}$ is unbiased for $\mu$. No distributional assumption is needed as long as the $X_i$ ‘s are distributed with the same mean $\mu$. Unbiasedness means that “on the average” our estimator is on target. Let us explain this last statement. If we repeat our drawing of a random sample of 1000 households, say 200 times, then we get $200 \bar{X}$ ‘s. Some of these $\bar{X}$ ‘s will be above $\mu$ some below $\mu$, but their average should be very close to $\mu$. Since in real life situations, we observe only one random sample, there is little consolation if our observed $\bar{X}$ is far from $\mu$. But the larger $n$ is, the smaller is the dispersion of this $\bar{X}$, since $\operatorname{var}(\bar{X})=\sigma^2 / n$ and the lesser is the likelihood of this $\bar{X}$ to be very far from $\mu$. This leads us to the concept of efficiency.
(ii) Efficiency
For two unbiased estimators, we compare their efficiencies by the ratio of their variances. We say that the one with lower variance is more efficient. For example, taking $\widehat{\mu}_1=X_1$ versus $\widehat{\mu}_2=\bar{X}$, both estimators are unbiased but $\operatorname{var}\left(\widehat{\mu}_1\right)=\sigma^2$ whereas, $\operatorname{var}\left(\widehat{\mu}_2\right)=\sigma^2 / n$ and $\left{\right.$ the relative efficiency of $\widehat{\mu}_1$ with respect to $\left.\widehat{\mu}_2\right}=$ $\operatorname{var}\left(\widehat{\mu}_2\right) / \operatorname{var}\left(\widehat{\mu}_1\right)=1 / n$, see Fig. 2.1. To compare all unbiased estimators, we find the one with minimum variance. Such an estimator if it exists is called the $M V U$ (minimum variance unbiased estimator). This is also called an efficient estimator. It is centered on the right target $\mu$ (because it is unbiased), and it has the tightest distribution around $\mu$ (because it has the smallest variance among all unbiased estimators). A lower bound for the variance of any unbiased estimator $\widehat{\mu}$ of $\mu$ is known in the statistical literature as the Cramér-Rao lower bound and is given by
$$\operatorname{var}(\widehat{\mu}) \geq 1 / n{E(\partial \log f(X ; \mu) / \partial \mu)}^2=-1 /\left{n E\left(\partial^2 \log f(X ; \mu) / \partial \mu^2\right)\right}$$
where we use either representation of the bound on the right hand side of (2.2) depending on which one is the simplest to derive.

## 经济代写|计量经济学代写Econometrics代考|Methods of Estimation

$$s^2=\sum_{i=1}^n\left(X_i-\bar{X}\right)^2 /(n-1)$$

(i) 矩量法

## 有限元方法代写

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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。