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Digital Library

of the European Council for Modelling and Simulation

 

Title:

Generalized Gamma Distributions As Mixed Exponential Laws And Related Limit Theorems

Authors:

Victor Korolev, Andrey Gorshenin, Alexander Korchagin, Alexander Zeifman

Published in:

 

 

 

(2017).ECMS 2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics

European Council for Modeling and Simulation. doi:10.7148/2017

 

 

ISBN: 978-0-9932440-4-9/

ISBN: 978-0-9932440-5-6 (CD)

 

 

31st European Conference on Modelling and Simulation,

Budapest, Hungary, May 23rd – May 26th, 2017

 

Citation format:

Victor Korolev, Andrey Gorshenin, Alexander Korchagin, Alexander Zeifman (2017). Generalized Gamma Distributions As Mixed Exponential Laws And Related Limit Theorems, ECMS 2017 Proceedings Edited by: Zita Zoltay Paprika, Péter Horák, Kata Váradi, Péter Tamás Zwierczyk, Ágnes Vidovics-Dancs, János Péter Rádics European Council for Modeling and Simulation. doi: 10.7148/2017-0642

 

DOI:

https://doi.org/10.7148/2017-0642

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.

 

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