On some new properties of the beta distribution
type: Item
instance of: scholarly article
title: On some new properties of the beta distribution
zbMATH Open document ID: 0951.62011
DOI: 10.1016/S0167-7152(98)00197-7
author: Włodzimierz Krysicki
published in: Statistics \& Probability Letters
publication date: 1999-03-30T00:00:00Z
review text: The paper considers new presentations of a random variable following the beta distribution as a finite or infinite product of independent random variables, each one following a specific gamma distribution. In addition a convergent infinite series of gamma variables is provided, as well as a modified version of the Mieshalkin-Rogozin, theorem. More specifically, the author derives the representation of the beta random variable as a product (finite or infinite) of gamma variables by using properties of the Mellin transform and the Gamma function. Thus a finite or infinite product representation of the gamma function allows for the use of the corresponding gamma random variables via the use of their Mellin transform. In the sequel, using such a representation, a specific series involving the logarithms of the Gamma variables is proved to be convergent. Finally a modification of a theorem given by Mieshalkin-Rogozin is used to find bounds for the distribution function of the beta distribution. The product representation, discussed previously, is useful for the derivation of this modified theorem.
reviewed by: Dimitris Karlis
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
zbMATH DE Number: 1271605
zbMATH Keywords: infinite convolutions
zbMATH Keywords: products of random variables
zbMATH Keywords: Mellin transform
zbMATH Keywords: Gamma function
MaRDI profile type: Publication
cites work: Fourier Transforms of Distribution Functions
cites work: Some Properties of Beta and Gamma Distributions
cites work: On groups of n independent random variables whose product follows the beta distribution
cites work: Q4131338
cites work: AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION
full work available at URL: s0167-7152(98)00197-7
OpenAlex ID: W2072819688
description: scientific article; zbMATH DE number 1271605