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Log-concavity of compound Poisson distributions. (English) Zbl 1463.60019

Summary: Log-concavity and total positivity of order 2 \((\mathrm{TP}_2)\) properties of two-parameter compound Poisson distributions \(Q(x|\theta, \nu)\) with respect to \(x\), \(\theta\) and \(\nu\) was studied by exploiting the interrelationships between log-concavity, \(\mathrm{TP}_2\) and reproductive property developed by the existing literatures. One application was also presented.

MSC:

60E05 Probability distributions: general theory
60E15 Inequalities; stochastic orderings
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