二项分布高阶原点矩的一种简便算法

辽宁石油化工大学学报 ›› 2008, Vol. 28 ›› Issue (1): 89-91.

二项分布高阶原点矩的一种简便算法

李金秋

辽宁石油化工大学理学院，辽宁抚顺 113001

收稿日期:2007-07-04 出版日期:2008-03-20 发布日期:2017-07-22

Simple Algorithm for the Binomial Distribution Moments on the Origin of Higher-Order

LI Jin-qiu

School of Science, Liaoning University of Petroleum & Chemical Technology, Fushun Liaoning 113001, P. R. China

Received:2007-07-04 Published:2008-03-20 Online:2017-07-22

摘要/Abstract

摘要： 考虑到直接用定义计算二项分布高阶原点矩的复杂性, 将组合数学中的第二类Stir ling 数应用到概率中, 给出了利用第二类S tirling 数求二项分布m 阶原点矩的方法:EX m = Σm l =0 S(m , l)[ n] l p l , 并用实例对此方法进行了验证。

关键词: 原点矩, 二项分布, 第二类Stirling数

Abstract: 　Conside ring the complexity on calculating the binomial distributio n moments on the origin o f hig her -o rder with definition , Stirling number o f the second kind o f combina to rics w as applied to pro bability .And a method in which Stir ling numbe r of the second kind w as used w as given to so lve this pro blem :EXm = Σm l =0 S(m , l)[ n] l p l .M oreo ver , the method w as tested by an example .

Key words: Moment on the origin, Binomial distribution, Stirling number

李金秋. 二项分布高阶原点矩的一种简便算法[J]. 辽宁石油化工大学学报, 2008, 28(1): 89-91.

LI Jin-qiu. Simple Algorithm for the Binomial Distribution Moments on the Origin of Higher-Order[J]. Journal of Liaoning Petrochemical University, 2008, 28(1): 89-91.