The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 43, Number 1 (1972), 242-250.
Families of Infinitely Divisible Distributions Closed Under Mixing and Convolution
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.
Ann. Math. Statist., Volume 43, Number 1 (1972), 242-250.
First available in Project Euclid: 27 April 2007
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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