离散型随机变量高阶原点矩的一种新的递推计算方法  

A New Recursive Calculation Method for the Higher Order Origin Moment of Discrete Random Variables

作　　者：徐晓岭 王蓉华[2] 顾蓓青 XU Xiao-ling;WANG Rong-hua;GU Bei-qing(School of Statistics and Information,Shanghai University of International Business and Economics,Shanghai 201620,China;Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620 [2]上海师范大学数理学院,上海200234

出　　处：《数学的实践与认识》2022年第2期263-272,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11671264);上海师范大学2021年国家自然科学基金培育计划项目(309-AC7001-21-003040);上海对外经贸大学应用统计学一流本科建设项目;上海市高校本科重点教改项目。

摘　　要：针对服从二项、泊松、几何、负二项、超几何、负超几何以及对数级数分布等离散型随机变量,给出了求其高阶原点矩的一个较为简单的递推计算方法.不仅非常容易地求出这些离散型随机变量的高阶原点矩,避免了计算阶乘矩或求导等复杂的运算,而且便于学生理解.论文还给出了这些离散型随机变量的3阶和4阶原点矩的表达式.A relatively simple recursive method is proposed for calculating the higher order origin moment of discrete random variables such as Binomial distribution,Poisson distribution,Geometric distribution,Negative binomial distribution,Hypergeometric distribution,Negative Hypergeometric distribution and Logarithmic series distribution.It’s not only easy to obtain the higher order origin moments of these discrete random variables,avoiding complex operations such as factorial moments or derivation,but also easy for students to understand.The expressions of the 3 rd and 4 th order origin moments of these discrete random variables are also given.

关 键 词：二项分布 泊松分布 几何分布 负二项分布 超几何分布 负超几何分布 原点矩 

分 类 号：O211.5[理学—概率论与数理统计]