Haight's distributions as a natural exponential family
type: Item
instance of: scholarly article
title: Haight's distributions as a natural exponential family
zbMATH Open document ID: 0633.62015
DOI: 10.1016/0167-7152(88)90115-0
author: Vanamamalai Seshadri
author: Gérard Letac
published in: Statistics \& Probability Letters
publication date: 1988-01-01T00:00:00Z
review text: In an index to the distributions of mathematical statistics, \textit{F. A. Haight} [J. Res. Nat. Bureau of Standards 65B(1), 23-60 (1961)] considers, without giving any references, the following distribution: \[ \alpha^{-1}\exp (-xe^{\alpha}\alpha^{- 1})\sum^{\infty}_{n=0}(n+1)^{n-1}(n!)^{-2}x^ n\mathbf{1}_{(0,\infty)}(x)dx\quad for\quad 0<\alpha <1. \] We show that these distributions belong to a large class of natural exponential families for which we compute the variance functions. These computations are then used to prove the infinite divisibility of Haight's distribution.
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E07
zbMATH DE Number: 4030698
zbMATH Keywords: natural exponential families
zbMATH Keywords: variance functions
zbMATH Keywords: infinite divisibility
MaRDI profile type: Publication
full work available at URL: 0167-7152(88)90115-0
OpenAlex ID: W2042229747
cites work: Index to the distributions of mathematical statistics
cites work: Natural exponential families with quadratic variance functions
description: scientific article; zbMATH DE number 4030698