概率论中几种具有可加性的分布及其关系汇总.doc

目录 TOC \o "1-5" \h \z 摘要 1 关键词 1 Abstract 1 Key words 1 引言 1 \o "Current Document" 1几种常见的具有可加性的分布 1 二项分布 2 泊松分布（Possion分布） 3 正态分布 4 伽玛分布 6 柯西分布 7 1.6卡方分布 7 \o "Current Document" 2具有可加性的概率分布间的关系 8 二项分布的泊松近似 8 二项分布的正态近似 9 正态分布与泊松分布间的关系 10 2.4正态分布与柯西分布、卡方分布及卡方分布与伽玛分布的关系 11 \o "Current Document" 3小结 12 参考文献 12 致谢 13 概率论中几种具有可加性的分布及其关系 概率论中几种具有可加性的分布及其关系 PAGE PAGE # PAGE PAGE # 概率论中几种具有可加性的分布及其关系 摘要 概率论与数理统计中概率分布的可加性是一个十分重要的内容 ?所谓分布的可加性指的是同一 类分布的独立随机变量和的分布仍属于此类分布 ?结合其特点，这里给出了概率论中几种具有可加性 的分布：二项分布，泊松分布，正态分布，柯西分布，卡方分布以及伽玛分布 ?文章讨论了各类分布 的性质及其可加性的证明，这里给出了证明分布可加性的两种方法，即利用卷积公式和随机变量的 特征函数?除此之外，文章就可加性分布之间的各种关系，如二项分布的泊松近似，棣莫佛 -拉普拉 斯中心极限定理等，进行了不同层次的讨论 关键词概率分布可加性相互独立 特征函数 Several Kinds of Probability Dstribution and its Relationship with Additive Abstract Probability and mathematical statistics in the probability distribution of additivity is a very important content.The distribution of the so-called additivity refers to the distribution of the same kind of independent random variables and distribution are still belong to this kind of distribution.Combined with its characteristics, here given several has additivity distribution in probability theory: the binomial distribution, poisson distribution and normal distribution and cauchy distribution, chi-square distribution and gamma distribution.Article discusses the nature of all kinds of distribution and its proof of additivity, additive of proof distribution are also given two methods, n amely using con voluti on formula and characteristic fun ctio n of a ran dom variable. In additi on, this paper the relati on ships betwee n the additive property distributi on, such as the binomial distribution of poisson approximation, Di mo - Laplace's central limit theorem, and so on, has carried on the differe nt levels of discussi on. Key Words probability distributionadditivity propertymutual in depe ndence Key Words probability distribution additivity property mutual in depe ndence characteristic funct