A NOTE ON THE CLOSURE OF CONVOLUTION POWER MIXTURES (RANDOM SUMS) OF EXPONENTIAL DISTRIBUTIONS

DOI10.1017/S1446788708000104zbMath1143.60028OpenAlexW2099804802MaRDI QIDQ3509968

J. M. P. Albin

Publication date: 25 June 2008

Published in: Journal of the Australian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s1446788708000104

zbMATH Keywords

exponential distributionTauberian theoremrandom sumcompound Poisson distributionconvolution power

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Asymptotic distribution theory in statistics (62E20) Laplace transform (44A10) Limit theorems in probability theory (60F99)

Related Items (15)

Randomly stopped sums of not identically distributed heavy tailed random variables ⋮ Closure properties of \(O\)-exponential distributions ⋮ Randomly stopped sums with consistently varying distributions ⋮ Closure property of consistently varying random variables based on precise large deviation principles ⋮ On the random max-closure for heavy-tailed random variables ⋮ On asymptotic equivalence among the solutions of some defective renewal equations ⋮ On closure properties of heavy-tailed distributions for random sums ⋮ Convolution and convolution-root properties of long-tailed distributions ⋮ Closure of some heavy-tailed distribution classes under random convolution ⋮ THE SUBEXPONENTIAL PRODUCT CONVOLUTION OF TWO WEIBULL-TYPE DISTRIBUTIONS ⋮ Randomly stopped maximum and maximum of sums with consistently varying distributions ⋮ Random convolution of O-exponential distributions ⋮ Randomly stopped sums with exponential-type distributions ⋮ Randomly stopped minima and maxima with exponential-type distributions ⋮ Tails of Stopped Random Products: The Factoid and Some Relatives

Cites Work

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• Asymptotics of infinitely divisible distributions on \({\mathbb{R}}\)
• On convolution tails
• Suprema and sojourn times of Lévy processes with exponential tails
• Functionals of infinitely divisible stochastic processes with exponential tails
• Infinite divisibility and generalized subexponentiality
• A Constrained Two-Dimensional Triangulation and the Solution of Closest Node Problems in the Presence of Barriers
• Subexponentiality and infinite divisibility
• Convolution Equivalence and Infinite Divisibility: Corrections and Corollaries

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