A new discrete distribution: The exponentiated discrete inverse Weibull distribution

Articles in Press

Document Type : Research Paper

Authors
Zahra Hamed Mashhadzadeh
S.M.T. Kamel MirMostafaee
Department of Statistics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
10.22075/ijnaa.2025.33690.5033
Abstract
‎Discrete distributions are used to model count data‎; ‎however‎, ‎at the same time‎, ‎they can play an important role in lifetime phenomena‎. ‎In this paper‎, ‎a new discrete distribution is proposed called the exponentiated discrete inverse Weibull distribution‎. ‎The new distribution includes several older distributions as special cases‎. ‎Several distributional properties of the new distribution, such as probability mass function‎, ‎hazard rate function‎, ‎moments‎, ‎skewness‎, ‎kurtosis‎, ‎and order statistics, are studied‎. ‎The new distribution can be a good candidate for modelling platykurtic data sets‎. ‎The problem of point estimation of the parameters based on the maximum likelihood method is discussed‎. ‎The asymptotic confidence intervals for the unknown parameters are obtained as well‎. ‎A simulation study is carried out to evaluate the maximum likelihood estimators and asymptotic confidence intervals‎. ‎A real data set is analyzed in order to show the applicability of the new distribution‎. ‎We end the paper with some remarks‎.
Keywords
‎Discrete inverse Weibull distribution‎
‎‎‎Maximum likelihood estimation‎
‎Moments‎
‎Order ‎statistics
‎Platykurtic ‎data.‎
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International Journal of Nonlinear Analysis and Applications

Articles in Press, Corrected Proof
Available Online from 12 July 2026

  • Receive Date 05 April 2024
  • Revise Date 21 November 2024
  • Accept Date 06 May 2025