一类Poisson型分布的特征

journal6 ›› 2000, Vol. 21 ›› Issue (2): 24-27.

一类Poisson型分布的特征

(天津师范大学数学系,天津 300073)

出版日期:2000-06-15 发布日期:2013-01-16
作者简介:邹华( 1965~ ) ,女,湖南省隆回县人,天津师范大学数学系讲师, 主要从事概率统计研究.

A Characteristics of A Class of Poisson Type Distribution

( Deparment of Mathematics, Tianjin Normal University, Tianjin 300073, China)

Online:2000-06-15 Published:2013-01-16

摘要/Abstract

摘要：证明了满足 EX²<∞ 的具有非退化分布的母体 X 服从 Poisson 型分布 P ( λ, α, 1)的充要条件是 T₂- T₁ 关于 T₁有常回归,其中 T₁= X =1nni= 1X_i, T₂=
1n- 1ni= 1( X_i- X )²分别为子样均值和子样方差.

关键词： 常回归, 条件数学期望, 解析特征函数, 累积量, 累积量母函数, Poisson型分布

Abstract: It is proved in this parper that population X of nonsingula distribut ion with EX²<∞ is of Poisson type dis-tribution P ( λ, α , 1) if and only i f the statistic T₂- T₁ has constantre gression on T _1, where T₁= X =1n ni= 1Xi is sample mean and T₂=1n- 1ni= 1(Xi - X )²is sample variance.

Key words: constant regression, conditional mathematical expectation, analytic characteristic function, cumulant, cumulant generat ing function, Poisson type distribution

邹华. 一类Poisson型分布的特征[J]. journal6, 2000, 21(2): 24-27.

ZOU Hua. A Characteristics of A Class of Poisson Type Distribution[J]. journal6, 2000, 21(2): 24-27.