AI Article Synopsis
- The text discusses the factorization of probability mass functions from Panjer's family of discrete distributions and their extensions to establish a stochastic order among these distributions.
- It presents key properties of this stochastic order and compares well-known distributions, leading to the creation of new distribution families that adhere to specific recurrence relations.
- The article derives recursion formulas for the probabilities of compound distributions within one of these new families and highlights applications in reliability theory.
Article Abstract
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 . 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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| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8791926 | PMC |
| http://dx.doi.org/10.1007/s00184-021-00822-5 | DOI Listing |
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