Abstract
In the present paper a family of discrete distributions is introduced through the probability generating function of any discrete distribution (generator). The properties of the family are systematically studied when the generator belongs to well-known families of discrete distributions (power series distributions, Bernoulli mixtures, Panjer family, Phase-type distributions). Applications are also provided in problems arising from the areas of reliability theory and start-up demonstration testing, which highlight the beneficial use of the family in order statistics related models.
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Acknowledgements
The authors wish to thank the referees for the thorough reading, useful comments and suggestions.
Funding
Work funded by National Matching Funds 2016-2017 of the Greek Government, and more specifically by the General Secretariat for Research and Technology (GSRT), related to EU project “ISMPH: Inference for a Semi-Markov Process (GA No 329128).
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Work done while VMK and SDD were postgraduate students at the Department of Statistics and Insurance Science, Greece.
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Koutras, V.M., Koutras, M.V. & Dafnis, S.D. A Family of Induced Distributions. Methodol Comput Appl Probab 24, 1833–1848 (2022). https://doi.org/10.1007/s11009-021-09887-1
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DOI: https://doi.org/10.1007/s11009-021-09887-1
Keywords
- Bernoulli mixtures
- Binomial-type distributions
- Panjer family
- Phase-type distributions
- Power series distributions
- reliability
- Start-up demonstration testing