A Family of Induced Distributions

Vasileios M. Koutras (), Markos V. Koutras () and Spiros D. Dafnis ()
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Vasileios M. Koutras: University of Piraeus
Markos V. Koutras: University of Piraeus
Spiros D. Dafnis: University of Piraeus

Methodology and Computing in Applied Probability, 2022, vol. 24, issue 3, 1833-1848

Abstract: 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.

Keywords: Bernoulli mixtures; Binomial-type distributions; Panjer family; Phase-type distributions; Power series distributions; reliability; Start-up demonstration testing; 60E05; 60J10 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11009-021-09887-1

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