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Dear allstaters, I appreciate very much directing me to a concrete references (books or papers) which prove the following for a discrete distribution with p.m.f p(x), x=0,1,2,... : 1. p(x) is log-convex ==> p(x) is convex 2. p(x) is log-convex ==> p(x) is infinitely divisible 3. p(x) is log-convex ==> R(x)=P(X >= x) is log-convex Thanks in advance. M.E. Ghitany %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%