New integrated view at partial-sums distributions

Abstract

Partial-sums discrete probability distributions occurred in description of many stochastic models.
They were used also as a tool for creating new distributions, or as a link between known distributions. It
is shown in this paper that every discrete distribution with only non-zero probabilities is a partial-sums
distribution, and, moreover, that it has innitely many parent distributions. The paper generalizes and
unies the concept of partial-sums distributions. Besides, it generalizes some risk models in insurance
and revises some approaches to mathematical modelling in quantitative linguistics.
Keywords: partial-sums distribution, Poisson distribution, hypergeometric series.