On a Parametrization of Partial-Sums Discrete Probability Distributions

Ján Mačutek, Gejza Wimmer and Michaela Koščová
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Ján Mačutek: Mathematical Institute, Slovak Academy of Sciences, Department of Mathematics, Constantine the Philosopher University in Nitra, 949 01 Nitra, Slovakia
Gejza Wimmer: Mathematical Institute, Slovak Academy of Sciences, 814 73 Bratislava, Slovakia
Michaela Koščová: Mathematical Institute, Slovak Academy of Sciences, 814 73 Bratislava, Slovakia

Mathematics, 2022, vol. 10, issue 14, 1-8

Abstract: For every discrete probability distribution, there is one and only one partial summation which leaves the distribution unchanged. This invariance property is reconsidered for distributions with one parameter. We show that if we change the parameter value in the function which defines the summation, two families of distributions can be observed. The first of them consists of distributions which are resistant to the change. For these distributions, the change of the parameter is reversed by the normalization constant, and the distributions remain unchanged. The other contains distributions sensitive to the change. Partial summations with the changed parameter value applied to sensitive distributions result in new distributions with two parameters. A necessary and sufficient condition for a distribution to be resistant to the parameter change is presented.

Keywords: discrete probability distributions; partial-sums distributions; invariance; distribution families (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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