Families of infinitely divisible distributions closed under mixing and convolution

J. Keilson, F.W. Steutel

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Abstract

Certain families of probability distribution functions maintain their infinite divisibility under repeated mixing and convolution. Examples on the continuum and lattice are given. The main tools used are Polya's criteria and the properties of log-convexity and complete monotonicity. Some light is shed on the relationship between these two properties.
Original languageEnglish
Pages (from-to)242-250
Number of pages9
JournalThe Annals of Mathematical Statistics
Volume43
Issue number1
DOIs
Publication statusPublished - 1972

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