PRESERVATION OF LOG-CONCAVITY UNDER CONVOLUTION
2017 ◽
Vol 32
(4)
◽
pp. 567-579
Keyword(s):
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.
2018 ◽
Vol 21
(2)
◽
pp. 633-645
Keyword(s):
2009 ◽
Vol 2009
◽
pp. 1-28
◽
2014 ◽
Vol 10
(1)
◽
pp. 53-62
◽
2003 ◽
Keyword(s):
2007 ◽
Vol 72
(615)
◽
pp. 169-172