负超几何及其推广分布的概率计算方法  

Probability computation methods of negative hypergeometric and its generalizations distribution

作　　者：王福昌[1] 贺财宝 WANG Fuchang;HE Caibao(Department of Basic Courses,Institute of Disaster Prevention Science and Technology,Sanhe 065201,China)

机构地区：[1]防灾科技学院基础部,河北三河065201

出　　处：《高师理科学刊》2023年第2期11-15,共5页Journal of Science of Teachers＇College and University

基　　金：廊坊市科技局科学研究与发展计划项目(2022011031)。

摘　　要：为避免计算负超几何分布的分布律时大阶乘计算导致的计算机上溢问题,利用Bernoulli数得到Stirling公式,给出n!的高精度近似表达式.利用负超几何分布的性质,推导出负超几何分布概率分布律的有效计算方法,并与R软件包的计算结果比较,验证了方法的正确性.同时,给出了最小负超几何分布和最大负超几何分布概率分布律的计算方法和相关的比较结果.In order to avoid the computer overflow problem caused by large factorial calculation when calculating the probability distribution of negative hypergeometric distribution,the Stirling formula is obtained by using Bernoulli number,and the high precision approximate expression of n! is given.Based on the property of negative hypergeometric distribution,an effective method to calculate the probability mass function of negative hypergeometric distribution is derived,the correctness of the method is verified by compared with calculation result of R software package.At the same time,the calculation method of probability mass function of minimum negative hypergeometric distribution and maximum negative hypergeometric distribution and the relative comparison results are given.

关 键 词：BERNOULLI数 STIRLING公式 负超几何分布 最小负超几何分布 最大负超几何分布 

分 类 号：O211[理学—概率论与数理统计]