A new extension of Poisson distribution for asymmetric count data: theory, classical and Bayesian estimation with application to lifetime data

Abdullah Alomair; Muhammad Ahsan-Ul-Haq

doi:10.7717/peerj-cs.1748

A new extension of Poisson distribution for asymmetric count data: theory, classical and Bayesian estimation with application to lifetime data

PeerJ Comput Sci. 2023 Dec 15:9:e1748. doi: 10.7717/peerj-cs.1748. eCollection 2023.

Authors

Abdullah Alomair¹, Muhammad Ahsan-Ul-Haq²

Affiliations

¹ Department of Quantitative Methods, School of Business, King Faisal University, Al-Ahsa, Saudi Arabia.
² College of Statistical Sciences, University of the Punjab, Lahore, Pakistan.

Abstract

Several research investigations have stressed the importance of discrete data analysis and its relevance to actual events. The current work focuses on a new discrete distribution with a single parameter that can be derived using the Poisson mixing technique. The new distribution is named the Poisson Entropy-Based Weighted Exponential Distribution. It is useful for discussing asymmetric "right-skewed" data with "heavy" tails. Its failure rate function can be used to explain situations with increasing failure rates. The statistical properties of the new distribution are expressed explicitly. The proposed model is simple to manage for under-, equal-, and over-dispersed datasets. The model parameters are estimated using the maximum likelihood method. We consider the parameter estimation for the new model based on right-censored data with a cure fraction. One more focus of the present study is the Bayesian estimation of the model parameters. In the end, three real-world dataset examples were utilized to show the value of the new distribution. These applications revealed that the new model outperforms other standard discrete models.

Keywords: Bayesian; Censoring; Data analysis; Dispersion; Estimation; Moments; Poisson-mixture.

Grants and funding

This work was supported by the Deanship of Scientific Research, Vice Presidency for Graduate Studies and Scientific Research, King Faisal University, Saudi Arabia [Grant No. 3479]. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.