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2018 | OriginalPaper | Buchkapitel

Gamma-Series Representations for the Sum of Independent Gamma Random Variables and for the Product of Independent Beta Random Variables

verfasst von : Filipe J. Marques

Erschienen in: Recent Studies on Risk Analysis and Statistical Modeling

Verlag: Springer International Publishing

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Abstract

In this work it is shown that using well-known series expansions it is possible to represent a single gamma distribution and also the logarithm of a single beta distribution, as an infinite mixture of gamma distributions. Then, using these representations, it is possible to derive simple gamma-series representations for the distribution of the sum of independent gamma random variables and for the sum of independent logbeta random variables, which by simple transformation may be used to represent also the distribution of the product of independent beta random variables. These representations may be used to develop accurate asymptotic approximations for corresponding distributions.

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Titel: Gamma-Series Representations for the Sum of Independent Gamma Random Variables and for the Product of Independent Beta Random Variables
verfasst von: Filipe J. Marques
Verlag: Springer International Publishing
Buch: Recent Studies on Risk Analysis and Statistical Modeling
Print ISBN: 978-3-319-76604-1

Electronic ISBN: 978-3-319-76605-8

Copyright-Jahr: 2018
DOI: https://doi.org/10.1007/978-3-319-76605-8_17

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