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An extended exponential hyper-Poisson distribution: Properties and applications

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  • C. Satheesh Kumar
  • A. S. Satheenthar

Abstract

Here we propose a new class of probability distributions as an extended version of the exponential hyper-Poisson distribution and Weibull Poisson distribution. We investigate several important aspects of the distribution through deriving expressions for its probability density function (pdf), cumulative distribution function, survival function, failure rate function, pdf of the order statistics, r-th raw moments, etc. The method of maximum likelihood estimation procedures along with EM algorithm is discussed for estimating the parameters of the distribution and a test procedure is suggested for testing the significance of the additional parameters of the proposed model. The use of the proposed distribution is illustrated through real-life data sets. Further, a brief simulation study is carried out for evaluating the performance of the estimators obtained for the parameters of the distribution.

Suggested Citation

  • C. Satheesh Kumar & A. S. Satheenthar, 2024. "An extended exponential hyper-Poisson distribution: Properties and applications," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(12), pages 4311-4333, June.
    • Handle: RePEc:taf:lstaxx:v:53:y:2024:i:12:p:4311-4333
    DOI: 10.1080/03610926.2023.2178261
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