The Annals of Mathematical Statistics

Families of Infinitely Divisible Distributions Closed Under Mixing and Convolution

J. Keilson and 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.

Article information

Source
Ann. Math. Statist., Volume 43, Number 1 (1972), 242-250.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177692717

Digital Object Identifier
doi:10.1214/aoms/1177692717

Mathematical Reviews number (MathSciNet)
MR298731

Zentralblatt MATH identifier
0242.60011

JSTOR
links.jstor.org

Citation

Keilson, J.; Steutel, F. W. Families of Infinitely Divisible Distributions Closed Under Mixing and Convolution. Ann. Math. Statist. 43 (1972), no. 1, 242--250. doi:10.1214/aoms/1177692717. https://projecteuclid.org/euclid.aoms/1177692717


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