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A Family of Induced Distributions

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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Corresponding author

Correspondence to Spiros D. Dafnis.

Additional information

Work done while VMK and SDD were postgraduate students at the Department of Statistics and Insurance Science, Greece.

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Cite this article

Koutras, V.M., Koutras, M.V. & Dafnis, S.D. A Family of Induced Distributions. Methodol Comput Appl Probab (2021). https://doi.org/10.1007/s11009-021-09887-1

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Keywords

  • Bernoulli mixtures
  • Binomial-type distributions
  • Panjer family
  • Phase-type distributions
  • Power series distributions
  • reliability
  • Start-up demonstration testing

Mathematics Subject Classification

  • 60E05
  • 60J10