Gamma分布与其它分布的若干定理

李智明

(新疆大学数学与系统科学学院,新疆乌鲁木齐 830046)

Gamma分布与其它分布的若干定理

李智明

(新疆大学数学与系统科学学院,新疆乌鲁木齐 830046)

利用条件概率的性质,得到Gamma分布与Poisson分布、广义负二项分布、广义Pareto分布的若干定理及推论.

条件概率;Gamma分布;Poisson分布;广义负二项分布;广义Pareto分布

基于文献[1-3]的Gamma分布与其它分布如:Poisson分布、广义负二项分布、广义Pareto分布等的定义,本文推导出它们之间的若干定理及推论.

2 Gamma分布与广义负二项分布的关系

定义4 称随机变量ξ服从参数为r,p的广义负二项分布(Generalized Negative Binominal Distribution),如果它的分布律为故结论成立.

3 Gamma分布与广义Praeto分布的关系

定义5 称随机变量ξ服从参数为r,s,β的广义Pareto分布(Generalized Pareto Distribution),如果它有概率密度为

除此之外,Gamma分布与Beta分布,Z分布有一定的关系,见[4].

[1] 周概容.概率论与数理统计[M].北京:高等教育出版社,1984:194-196.

[2] M ichael A Bean.Probability:the science of uncertainty w ith app lications to investments,insurance and engineering [M].Beijing:China Machine Press,2003:221-234.

[3] Norman L Johnson,Samuel Kotz.Distribution in statistics:continuous univariate distribution-1[M].New York: Wiley&Son,1970:166-172.

[4] 茆诗松,王静龙,等.高等数理统计[M].北京:高等教育出版社,2006:7-82.

Some Theoremsabout Gamma Distribution and Other D istributions

LIZhi-ming
(College of Mathematics and System Sciences,Xinjiang University,U rumqi 830046,China)

Using the p roperties of conditional p robability,this article gained some theo rem s and co rollaries about Gamma distribution and Poisson distribution,generalized negative binominal and generalized Pareto distribution.

conditional p robability;Gamma distribution;Poisson distribution;generalized negative binominal distribution;generalized Pareto distribution

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1672-1454(2010)03-0185-04

2007-11-01