The Annals of Probability

On Log-Concave and Log-Convex Infinitely Divisible Sequences and Densities

Bjorn G. Hansen

Full-text: Open access

Abstract

We consider nonnegative infinitely divisible random variables whose Levy measures are either absolutely continuous or supported by the integers. Necessary conditions are found ensuring that such distributions are $\log$-concave or $\log$-convex.

Article information

Source
Ann. Probab., Volume 16, Number 4 (1988), 1832-1839.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176991600

Digital Object Identifier
doi:10.1214/aop/1176991600

Mathematical Reviews number (MathSciNet)
MR958219

Zentralblatt MATH identifier
0659.60030

JSTOR
links.jstor.org

Subjects
Primary: 60E07: Infinitely divisible distributions; stable distributions

Keywords
Infinitely divisible distribution discrete distribution absolutely continuous distribution strongly unimodal log-concave log-convex completely monotone

Citation

Hansen, Bjorn G. On Log-Concave and Log-Convex Infinitely Divisible Sequences and Densities. Ann. Probab. 16 (1988), no. 4, 1832--1839. doi:10.1214/aop/1176991600. https://projecteuclid.org/euclid.aop/1176991600


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