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PRESERVATION OF LOG-CONCAVITY UNDER CONVOLUTION

Part of: Distribution theory - Probability

Published online by Cambridge University Press:  26 September 2017

Tiantian Mao ,
Wanwan Xia  and
Taizhong Hu
Tiantian Mao
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China Hefei, Anhui 230026, China E-mail: tmao@ustc.edu.cn; xiaww@mail.ustc.edu.cn; thu@ustc.edu.cn
Wanwan Xia
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China Hefei, Anhui 230026, China E-mail: tmao@ustc.edu.cn; xiaww@mail.ustc.edu.cn; thu@ustc.edu.cn
Taizhong Hu
Affiliation:
Department of Statistics and Finance, School of Management, University of Science and Technology of China Hefei, Anhui 230026, China E-mail: tmao@ustc.edu.cn; xiaww@mail.ustc.edu.cn; thu@ustc.edu.cn
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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.

Keywords

exponential distributiongeometric distributionnegatively binomial distributionnormal distributionPoisson distribution

MSC classification

Secondary: 60E05: Distributions
Type
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 

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