On the log-concavity of the Mittag-Leffler distribution

26.01.2023 17:00 - 17:45

Thomas Simon (University of Lille, FR)

Abstract: The Mittag-Leffler random variable is the positive random variable whose moment generating function is the classical Mittag-Leffler function with parameter α (0,1). In this talk, we consider basic distributional properties of this random variable which appears in various domains of probability theory. In particular, we show that its density is log-concave if and only if α ≤ α, where α = 0.771667... is some threshold defined implicitly with the Gamma functions, and that this property is equivalent to the reciprocal convexity on the negative half-line of the associated Mittag-Leffler function. We will also discuss some extensions of these results to the more general Wright functions of the second kind and their associated two-parameter Mittag-Leffler functions.

WU Vienna, Welthandelsplatz 1, 1020 Wien, ground floor, SR D4.0.039