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Duals of convolution thinned relationships

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  • M. C. Jones

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.

Suggested Citation

  • M. C. Jones, 2024. "Duals of convolution thinned relationships," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(3), pages 563-568, August.
    • Handle: RePEc:bla:stanee:v:78:y:2024:i:3:p:563-568
    DOI: 10.1111/stan.12337
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    1. Jones, M.C., 2022. "Duals of multiplicative relationships involving beta and gamma random variables," Statistics & Probability Letters, Elsevier, vol. 191(C).
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