Paper Info
Title
Generalized Gamma Distributions As Mixed Exponential Laws And Related Limit Theorems
Abstract
A theorem due to L. J. Gleser stating that a gamma distribution with shape parameter no greater than one is a mixed exponential distribution is extended to generalized gamma distributions introduced by E. W. Stacy as a special family of lifetime distributions containing both gamma distributions, exponential power and Weibull distributions. It is shown that the mixing distribution is a scale mixture of strictly stable laws concentrated on the nonnegative halfline. As a corollary, the representation is obtained for the mixed Poisson distribution with the generalized gamma mixing law as a mixed geometric distribution. Limit theorems are proved establishing the convergence of the distributions of statistics constructed from samples with random sizes obeying the mixed Poisson distribution with the generalized gamma mixing law including random sums to special normal mixtures.
Year
Venue
Keywords
2017
PROCEEDINGS - 31ST EUROPEAN CONFERENCE ON MODELLING AND SIMULATION ECMS 2017
Generalized gamma distribution, Weibull distribution, mixed exponential distribution, mixed Poisson distribution, mixed geometric distribution, strictly stable distribution, normal mixture, random sum, random sample size
Field
DocType
Citations 
Discrete mathematics,Exponential function,Natural exponential family,Generalized integer gamma distribution,Pure mathematics,Generalized beta distribution,Gamma distribution,Generalized gamma distribution,Mathematics
Conference
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Victor Korolev11611.26
Andrey Gorshenin213.67
Alexander Yu. Korchagin300.34
Alexander I. Zeifman44417.93