Duals of convolution thinned relationships

Jones, M. C. (2024). Duals of convolution thinned relationships. Statistica Neerlandica (Early access).

DOI: https://doi.org/10.1111/stan.12337

Abstract

In a recent article, J. Peyhardi gives a number of novel results related to quasi Pólya thinning which encompass a number of important mixture relationships between univariate discrete distributions. In this note, I explore the duals of the general results on convolution thinning given in Peyhardi's Theorem 1 in order to obtain new relationships and to gain new insights into old relationships. Some consequences—for integer‐valued autoregressive processes—and analogues—in the continuous case—are noted.

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