<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 infinitely many parent distributions. The paper generalizes and unifies the concept of partial-sums distribution. Besides, it generalizes some risk models in insurance and revises some approaches to mathematical modelling in quantitative linguistics.</p></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 infinitely many parent distributions. The paper generalizes and unifies the concept of partial-sums distribution. Besides, it generalizes some risk models in insurance and revises some approaches to mathematical modelling in quantitative linguistics.

New integrated view at partial-sums distributions

Institute of Mathematics and Statistics Masaryk University Kotl´aˇrsk´a 2 CZ–611-37 Brno CZECH REPUBLIC

Mathematical Institute Slovak Academy of Sciences ˇStef´anikova 49 SK–814-73 Bratislava SLOVAKIA

Faculty of Natural Sciences Matej Bel University Tajovsk´eho 40 SK–974-01 Bansk´a Bystrica SLOVAKIA

Department of Applied Mathematics and Statistics Faculty of Mathematics, Physics and Informatics Comenius University Mlynsk´a dolina SK–842-48 Bratislava SLOVAKIA

Tatra Mountains Mathematical Publications

{"article-title":"New integrated view at partial-sums distributions"}

Partial-sums discrete probability distributions occurred in description of many stochastic models. They were used also as a tool for creating new...

New integrated view at partial-sums distributions

Published Online: Nov 13, 2012

Page range: 183 - 190

DOI: https://doi.org/10.2478/v10127-012-0018-8

Keywords
partial-sums distribution, Poisson distribution, hypergeometric series.

This content is open access.

New integrated view at partial-sums distributions

Published Online: Nov 13, 2012

Page range: 183 - 190

DOI: https://doi.org/10.2478/v10127-012-0018-8

Keywordspartial-sums distribution, Poisson distribution, hypergeometric series.

This content is open access.

Keywords
partial-sums distribution, Poisson distribution, hypergeometric series.