Gamma分布與其它分布的若干定理

李智明

(新疆大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院,新疆烏魯木齊 830046)

Gamma分布與其它分布的若干定理

李智明

(新疆大學(xué)數(shù)學(xué)與系統(tǒng)科學(xué)學(xué)院,新疆烏魯木齊 830046)

利用條件概率的性質(zhì),得到Gamma分布與Poisson分布、廣義負(fù)二項(xiàng)分布、廣義Pareto分布的若干定理及推論.

條件概率;Gamma分布;Poisson分布;廣義負(fù)二項(xiàng)分布;廣義Pareto分布

基于文獻(xiàn)[1-3]的Gamma分布與其它分布如:Poisson分布、廣義負(fù)二項(xiàng)分布、廣義Pareto分布等的定義,本文推導(dǎo)出它們之間的若干定理及推論.

2 Gamma分布與廣義負(fù)二項(xiàng)分布的關(guān)系

定義4 稱隨機(jī)變量ξ服從參數(shù)為r,p的廣義負(fù)二項(xiàng)分布(Generalized Negative Binominal Distribution),如果它的分布律為故結(jié)論成立.

3 Gamma分布與廣義Praeto分布的關(guān)系

定義5 稱隨機(jī)變量ξ服從參數(shù)為r,s,β的廣義Pareto分布(Generalized Pareto Distribution),如果它有概率密度為

除此之外,Gamma分布與Beta分布,Z分布有一定的關(guān)系,見[4].

[1] 周概容.概率論與數(shù)理統(tǒng)計(jì)[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] 茆詩松,王靜龍,等.高等數(shù)理統(tǒng)計(jì)[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