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A Family of Induced Distributions

Author

Listed:
  • Vasileios M. Koutras

    (University of Piraeus)

  • Markos V. Koutras

    (University of Piraeus)

  • Spiros D. Dafnis

    (University of Piraeus)

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.

Suggested Citation

  • Vasileios M. Koutras & Markos V. Koutras & Spiros D. Dafnis, 2022. "A Family of Induced Distributions," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1833-1848, September.
    • Handle: RePEc:spr:metcap:v:24:y:2022:i:3:d:10.1007_s11009-021-09887-1
    DOI: 10.1007/s11009-021-09887-1
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    References listed on IDEAS

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    1. Markos V. Koutras & Serkan Eryilmaz, 2017. "Compound Geometric Distribution of Order k," Methodology and Computing in Applied Probability, Springer, vol. 19(2), pages 377-393, June.
    2. Philippou, Andreas N. & Georghiou, Costas & Philippou, George N., 1983. "A generalized geometric distribution and some of its properties," Statistics & Probability Letters, Elsevier, vol. 1(4), pages 171-175, June.
    3. Frosso S. Makri & Zaharias M. Psillakis, 2011. "On Success Runs of Length Exceeded a Threshold," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 269-305, June.
    4. N. Balakrishnan & M.V. Koutras & F.S. Milienos, 2014. "Start‐up demonstration tests: models, methods and applications, with some unifications," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 373-413, July.
    5. Eryilmaz, Serkan & Kan, Cihangir, 2019. "Reliability and optimal replacement policy for an extreme shock model with a change point," Reliability Engineering and System Safety, Elsevier, vol. 190(C), pages 1-1.
    6. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00443846, HAL.
    7. Narayanaswamy Balakrishnan & M.V. Koutras & F.S. Milienos, 2014. "Authors’ rejoinder “Start‐up demonstration tests: models, methods, and applications, with some unifications”," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 30(4), pages 427-428, July.
    8. EryIlmaz, Serkan, 2011. "Joint distribution of run statistics in partially exchangeable processes," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 163-168, January.
    9. Spiros D. Dafnis & Frosso S. Makri & Markos V. Koutras, 2021. "Generalizations of Runs and Patterns Distributions for Sequences of Binary Trials," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 165-185, March.
    10. Eryilmaz, Serkan & Devrim, Yilser, 2019. "Reliability and optimal replacement policy for a k-out-of-n system subject to shocks," Reliability Engineering and System Safety, Elsevier, vol. 188(C), pages 393-397.
    11. Hess, Klaus Th. & Liewald, Anett & Schmidt, Klaus D., 2002. "An Extension of Panjer's Recursion," ASTIN Bulletin, Cambridge University Press, vol. 32(2), pages 283-297, November.
    12. Dominique Guegan & Bertrand Hassani, 2009. "A modified Panjer algorithm for operational risk capital calculations," Post-Print halshs-00443846, HAL.
    13. Boutsikas, M. V. & Koutras, M. V., 2002. "Modeling claim exceedances over thresholds," Insurance: Mathematics and Economics, Elsevier, vol. 30(1), pages 67-83, February.
    14. Koutras, Vasileios M. & Koutras, Markos V. & Yalcin, Femin, 2016. "A simple compound scan statistic useful for modeling insurance and risk management problems," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 202-209.
    15. Vasileios M. Koutras & Markos V. Koutras, 2020. "Exact Distribution of Random Order Statistics and Applications in Risk Management," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1539-1558, December.
    16. Eisele, Karl-Theodor, 2006. "Recursions for compound phase distributions," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 149-156, February.
    17. Panjer, Harry H., 1981. "Recursive Evaluation of a Family of Compound Distributions," ASTIN Bulletin, Cambridge University Press, vol. 12(1), pages 22-26, June.
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