摘要自提出以来, 关于中心极限定理的内容在学术界早已相当丰富，它不仅在概率论中 相当重要，当进行大样本统计推断时，它更是非常重要的理论基础。该定理实质内容即论 证大量随机变量之和的极限分布是正态分布，而通常所说的中心极限定理就是证明该部 分内容的相关定理的总称，课题所要研究的定理即为林德伯格－列维定理，即独立同分布 情形下随机变量和的中心极限定理。为了演示该定理，可以通过随机模拟的方法，通过该 方法可以对列维定理进行很好的演示。通过控制随机变量个数，使其合理地增大。分析随 机变量个数逐渐增大时，随机变量和的中心极限定理的收敛情况。并且对不同分布进行模 拟，来客观说明列维定理对不同分布的普适性。76142

毕业论文关键词 中心极限定理 随机变量 独立同分布 随机模拟 随机数 Matlab

Title Approximation degree analysis of the central limit theorem for the independent identically distributed random variables based on the stochastic simulation

method Abstract  Since the central limit theorem has been proposed, the content is very rich。 It is not only an important part of the theory of probability, but also a theoretical basis for the statistical inference of large samples。 The essential content of central limit theorem is to prove that the limit distribution of a large number of random variables is normal distribution, and the central limit theorem is the general term for the relevant theorem to demonstrate the part。 The theorem to be studied is the Levi Lindberg theorem, which is the central limit theorem of the sum of independent identically distributed random variables。 In order to demonstrate the theorem, we can use the method of stochastic simulation, and the method can be used to demonstrate the Levi theorem。 By controlling the number of random variables, so that it is reasonable to increase。 We analyze the convergence of the central limit theorem for random variables when the number of random variables are gradually increased。 And the different probability distribution was simulated to illustrate that Levi's theorem is universal to different distribution。

Keywords central limit theorem, random variable, independent    identically distributed, stochastic simulation, random number, Matlab

目 次

1 绪论 1

1。1 课题研究背景及目的 1

1。1。1 中心极限定理研究相关背景及目的 1

1。1。2 随机模拟研究背景及目的 1

1。2 研究现状 2

1。3 研究内容 2

2 预备知识 3

3 中心极限定理的相关证明 5

4 随机模拟方法 8

4。1 影响随机模拟方法精度的因素 8