Strongly unimodal distributions with the support in $\mathbb{R}_+$

Yu. P. Virchenko^a, A. M. Tevolde<sup>b

a</sup> Belgorod Shukhov State Technological University
^b Belgorod State University

Abstract: In this paper, we consider strongly unimodal distribution functions $V$ whose supports are concentrated on $\mathbb{R}_+ \equiv [0, \infty)$ introduced by I. A. Ibragimov. Such distributions preserve the unimodality property when it is convoluted with any unimodal distribution function. We prove that a sufficient condition of strong unimodality of a distribution is the existence of a finite first statistical moment. In particular, the class of such distributions contains absolutely continuous and logarithmically convex distributions.

Keywords: convolution of distributions, logarithmic concavity, nonnegative random variable, unimodal distribution, strong unimodality

UDC: 519.213

MSC: 60E05

DOI: 10.36535/2782-4438-2025-245-24-37