This paper presents a brief review of the logconcavity of some compound distributions and its relationship to Turán-type inequalities. Further, we introduce a new concept of twice-logconcavity (twice-logconvexity) and show… Click to show full abstract
This paper presents a brief review of the logconcavity of some compound distributions and its relationship to Turán-type inequalities. Further, we introduce a new concept of twice-logconcavity (twice-logconvexity) and show that many discrete probability distributions and combinatorial sequences are twice-logconcave. These results are closely related to other areas of mathematics such as combinatorics and analysis.
               
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