An extended exponential hyper-Poisson distribution: Properties and applications

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.

Keywords:

• Compounding
• EM algorithm
• maximum likelihood estimation
• positive hyper-poisson distribution
• simulation
• Weibull distribution

Acknowledgments

Authors are highly thankful to the Editor-in-chief, the Associate Editor and the anonymous Referees for their valuable comments that greatly improved the quality and presentation of the manuscript. The first author is particularly thankful to Department of Science and Technology, New Delhi (Governmet of India) for financial support (MTR/2017/000942). The second author is CSIR-SRF thankful to the Council of Scientific and Industrial Research (CSIR), New Delhi for financial assistance (File No: 09/102(0263)/2019-EMR-I).