On a stochastic order induced by an extension of Panjer’s family of discrete distributions

We factorize probability mass functions of discrete distributions belonging to Panjer’s family and to its certain extensions to define a stochastic order on the space of distributions supported on [Formula: see text] . Main properties of this order are presented. Comparison of some well-known distri...

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Autores principales: Beknazaryan, Aleksandr, Adamic, Peter
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8791926/
https://www.ncbi.nlm.nih.gov/pubmed/35125519
http://dx.doi.org/10.1007/s00184-021-00822-5
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author Beknazaryan, Aleksandr
Adamic, Peter
author_facet Beknazaryan, Aleksandr
Adamic, Peter
author_sort Beknazaryan, Aleksandr
collection PubMed
description We factorize probability mass functions of discrete distributions belonging to Panjer’s family and to its certain extensions to define a stochastic order on the space of distributions supported on [Formula: see text] . Main properties of this order are presented. Comparison of some well-known distributions with respect to this order allows to generate new families of distributions that satisfy various recurrrence relations. The recursion formula for the probabilities of corresponding compound distributions for one such family is derived. Applications to various domains of reliability theory are provided.
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spelling pubmed-87919262022-02-02 On a stochastic order induced by an extension of Panjer’s family of discrete distributions Beknazaryan, Aleksandr Adamic, Peter Metrika Article We factorize probability mass functions of discrete distributions belonging to Panjer’s family and to its certain extensions to define a stochastic order on the space of distributions supported on [Formula: see text] . Main properties of this order are presented. Comparison of some well-known distributions with respect to this order allows to generate new families of distributions that satisfy various recurrrence relations. The recursion formula for the probabilities of corresponding compound distributions for one such family is derived. Applications to various domains of reliability theory are provided. Springer Berlin Heidelberg 2021-05-13 2022 /pmc/articles/PMC8791926/ /pubmed/35125519 http://dx.doi.org/10.1007/s00184-021-00822-5 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Beknazaryan, Aleksandr
Adamic, Peter
On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title_full On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title_fullStr On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title_full_unstemmed On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title_short On a stochastic order induced by an extension of Panjer’s family of discrete distributions
title_sort on a stochastic order induced by an extension of panjer’s family of discrete distributions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8791926/
https://www.ncbi.nlm.nih.gov/pubmed/35125519
http://dx.doi.org/10.1007/s00184-021-00822-5
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