四种常用概率分布间的极限关系及近似逼近探究  

Exploring the Limit Relationship and Approximation of Four Commonly Used Probability Distributions

作　　者：刘发江 李开艳 撒靓瑶 LIU Fajiang;LI Kaiyan;SHA Jingyao(School of Mathematics and Statistics,Zhaotong University,Zhaotong 657000,China;School of Intelligent Manufacturing,Zhaotong Vocational College,Zhaotong 657000,China)

机构地区：[1]昭通学院数学与统计学院,云南昭通657000 [2]昭通职业学院智能制造学院,云南昭通657000

出　　处：《昭通学院学报》2024年第5期35-38,共4页Journal of Zhaotong University

基　　金：昭通学院课程思政示范项目资助。

摘　　要：本文讨论了概率论与数理统计课程中超几何分布、二项分布、泊松分布和正态分布这四种常用概率分布之间的极限关系;并指出在概率计算中,一定条件下超几何分布可以用二项分布近似、二项分布可以用泊松分布和正态分布近似、泊松分布也可以用正态分布近似.最后,用关系结构图展示了几种常用分布的内在关系,帮助学生更好地理解和使用几种概率分布,建立相对完整的知识体系.This paper discusses the limit relation between four commonly used probability distributions in probability theory and mathematical statistics courses:hypergeometric distribution,binomial distribution,Poisson distribution,and normal distribution.And it is pointed out that in probability calculation,under certain conditions,hypergeometric distribution can be approximated by binomial distribution,binomial distribution can be approximated by Poisson distribution and normal distribution,and Poisson distribution can also be approximated by normal distribution.Finally,a structural diagram was used to demonstrate the intrinsic relationships of several commonly used distributions,in order to help students better understand and use several probability distributions,and establish a relatively complete knowledge system.

关 键 词：超几何分布 二项分布 泊松分布 正态分布 极限分布 

分 类 号：G642[文化科学—高等教育学]