Stein方法在求解随机变量线性组合概率分布中的应用

Application of Stein method in solving linear combination probability distribution of random variables

摘要

给出一种基于改进后的Stein方程求解随机变量线性组合概率分布的证明方法.基于随机变量Z_r和$\widetilde{Z}_{r}$的线性组合H=m^-1Z_r+n^-1$\widetilde{Z}_{r}$,利用伽马分布$\Gamma$(r,1)的Stein特征,求得关于H的Stein方程;加入二次可微函数,并采用改进后的Stein方程,求得H₊和H_-概率密度函数及显示公式.

Abstract

This paper presents a method to prove the probability distribution of linear combinations of random variables based on the modified Stein equation. Based on the linear combination H=m^-1Z_r+n^-1$\widetilde{Z}_{r}$ of random variables Z_r and $\widetilde{Z}_{r}$, Stein equation about H is obtained by using the Stein feature of gamma distribution $\Gamma$(r,1). By adding the quadratic differentiable function and using the improved Stein equation, the probability density function and the display formula about H₊ and H_- are obtained.

关键词

伽马分布 / 概率密度函数 / Stein方法

Key words

gamma distribution / probability density function / Stein method

参考文献

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基金资助

2020年辽宁省教育厅项目(JYT20L03)