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Natural Discrete One Parameter Polynomial Exponential Family of Distributions and the Application

Author

Listed:
  • Sudhansu S. Maiti

    (Visva-Bharati University)

  • Molay Kumar Ruidas

    (Triveni Devi Bhalotia College)

  • Sumanta Adhya

    (West Bengal State University)

Abstract

A new natural discrete version of the one-parameter polynomial exponential family of distributions called Natural Discrete One Parameter Polynomial Exponential (NDOPPE) distribution has been proposed and studied. Structural and reliability properties have been studied. The estimation procedure of the parameter of the distribution has been mentioned. Compound NDOPPE distribution in the context of the collective risk model in closed form has been obtained. The suitability of modelling extreme data using this compound distribution has been worked out with the help of some automobile claims. The fitted model is compared with the already available compound versions of classical Poisson, Negative binomial, discrete Lindley, xgamma-I and xgamma-II distributions.

Suggested Citation

  • Sudhansu S. Maiti & Molay Kumar Ruidas & Sumanta Adhya, 2024. "Natural Discrete One Parameter Polynomial Exponential Family of Distributions and the Application," Annals of Data Science, Springer, vol. 11(3), pages 1051-1076, June.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:3:d:10.1007_s40745-022-00422-8
    DOI: 10.1007/s40745-022-00422-8
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