## The Annals of Probability

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

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

#### 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