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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