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Hirschman-Widder densities

Belton, A and Guillot, D and Khare, A and Putinar, M (2022) Hirschman-Widder densities. In: Applied and Computational Harmonic Analysis, 60 . pp. 396-425.

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


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. © 2022 Elsevier Inc.

Item Type: Journal Article
Publication: Applied and Computational Harmonic Analysis
Publisher: Academic Press Inc.
Additional Information: The copyright for this article belongs to Authors
Keywords: Polynomials, Hypoexponential distribution; Linear combinations; Point wise; Polya frequency; Polya frequency function; Polynomial functions; Positive integers; Probability densities; Totally positive; Totally positive function, Exponential functions
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 19 May 2022 05:27
Last Modified: 19 May 2022 05:27
URI: https://eprints.iisc.ac.in/id/eprint/71977

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