PRESERVATION OF LOG-CONCAVITY UNDER CONVOLUTION

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 F the set of distributions G such that the convolution of F and G has a log-concave probability mass function or probability den...

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Published inProbability in the engineering and informational sciences Vol. 32; no. 4; pp. 567 - 579
Main Authors Mao, Tiantian, Xia, Wanwan, Hu, Taizhong
Format Journal Article
LanguageEnglish
Published New York, USA Cambridge University Press 01.10.2018
Subjects
Concavity
Convolution
Normal distribution
Probability density functions
Random variables
negatively binomial distribution
normal distribution
exponential distribution
Poisson distribution
geometric distribution
60E05
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Summary: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 F 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 F ⊆ G, where F and G belong to a parametric family of distributions. Both discrete and continuous settings are considered.
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ISSN:0269-9648
1469-8951
DOI:10.1017/S0269964817000389