Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Filipe J. Marques, M. Theodor Loots, Andriëtte Bekker

Research output: Contribution to journalArticle

Abstract

Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.

Original languageEnglish
Pages (from-to)718-5735
JournalMathematical Methods in the Applied Sciences
Volume42
Issue number17
DOIs
Publication statusPublished - 30 Nov 2019

Keywords

  • binomial theorem
  • exponential expansion
  • generalized gamma distribution
  • mixtures

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