离散型随机变量k阶矩的计算  

Calculation of k-th moment of Discrete Random Variables

作　　者：何刚[1] 吴文青[2] 夏杰 HE Gang;WU Wen-qing;XIA Jie(School of Computer Science and Technology,Southwest University of Science and Technology,Mianyang 621010,China;School of Science,Southwest University of Science and Technology,Mianyang 621010,China)

机构地区：[1]西南科技大学计算机科学与技术学院,四川绵阳621010 [2]西南科技大学理学院,四川绵阳621010

出　　处：《数学的实践与认识》2019年第18期323-328,共6页Mathematics in Practice and Theory

基　　金：西南科技大学素质类教改项目(16xnsu06);西南科技大学龙山学术人才科研支持计划基金(17LZXY20);西南科技大学博士研究基金资助项目(16zx7108,15zx7141)

摘　　要：讨论了离散型随机变量k阶矩的计算问题·利用概率母函数和第一类Stirling数推导了k阶矩满足的统一递推表达式,并以常见的四种离散分布:二项分布、几何分布、泊松分布和负二项分布为例,借助数学计算软件mathematica给出了各自的前6阶矩的具体表达式.This paper discusses the calculation of the k-th moment for discrete random variables.The unified recursive expressions for the k-th moment are derived by using the probability generating function and the Stirling numbers of the first kind.Further,the four discrete distributions:Binomial distribution,geometric distribution,Poisson distribution,and negative binomial distribution are detailed discussed with the help of the Mathematica software,and the specific expressions of their first six moments are given respectively.

关 键 词：离散随机变量 概率母函数 第一类STIRLING数 矩 

分 类 号：O211.5[理学—概率论与数理统计]