多项分布与Dirichlet分布概率的相互表示

Mutual Expressions Between Probabilities of Multinomial Distributions and Probabilities of Dirichlet Distributions

讨论了四种多项分布尾概率与四种Dirichlet分布尾概率的相互表示,并将结果应用于Majorization理论,得到了多项分布和Dirichlet分布对应的一些性质.同时,结果可应用于多项分布最大、最小参数的贝叶斯推断,在佛罗里达州沃尔顿县白人和黑人的职业状态调查结果中,求出最大、最小参数的后验分布函数以及95%贝叶斯区间估计,模拟结果表明提供的方法具有较好的表现.

In this paper,we discuss the mutual representation between the tail probability of four kinds of multinomial distributions and the tail probability of four Dirichlet distributions,and the results are applied to the majorization theory,a number of properties corresponding to the Multinomial distribution and Dirichlet distribution are obtained.At the same time,the results are applied to the Bayesian inference with the largest and smallest parameters.In the investigation result of the occupational status of white and black people in Walton County,Florida,we calculate the posterior distribution function of the maximum and minimum parameters as well as 95%Bayesian interval estimation,the simulation results show that this method performs well.