Hirschman–Widder densities

Belton, Alexander ; Guillot, Dominique ; Khare, Apoorva ; Putinar, Mihai (2022) Hirschman–Widder densities Applied and Computational Harmonic Analysis, 60 . pp. 396-425. ISSN 1063-5203

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Official URL: http://doi.org/10.1016/j.acha.2022.04.002

Related URL: http://dx.doi.org/10.1016/j.acha.2022.04.002

Abstract

Hirschman and Widder introduced a class of Pólya frequency functions given by linear combinations of one-sided exponential functions. The members of this class are probability densities, and the class is closed under convolution but not under pointwise multiplication. We show that, generically, a polynomial function of such a density is a Pólya frequency function only if the polynomial is a homothety, and also identify a subclass for which each positive-integer power is a Pólya frequency function. We further demonstrate connections between the Maclaurin coefficients, the moments of these densities, and the recovery of the density from finitely many moments, via Schur polynomials.

Item Type:Article
Source:Copyright of this article belongs to Elsevier Science.
Keywords:Polya frequency function; Totally positive function; Hypoexponential distribution
ID Code:127087
Deposited On:17 Oct 2022 05:18
Last Modified:17 Oct 2022 05:18

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