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PRESERVATION OF LOG-CONCAVITY UNDER CONVOLUTION
Published online by Cambridge University Press: 26 September 2017
Abstract
Log-concave random variables and their various properties play an increasingly important role in probability, statistics, and other fields. For a distribution F, denote by 𝒟F the set of distributions G such that the convolution of F and G has a log-concave probability mass function or probability density function. In this paper, we investigate sufficient and necessary conditions under which 𝒟F ⊆ 𝒟G, where F and G belong to a parametric family of distributions. Both discrete and continuous settings are considered.
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- Research Article
- Information
- Probability in the Engineering and Informational Sciences , Volume 32 , Issue 4 , October 2018 , pp. 567 - 579
- Copyright
- Copyright © Cambridge University Press 2017