A discrete analogue of odd Weibull-G family of distributions: properties, classical and Bayesian estimation with applications to count data

M El-Morshedy; M S Eliwa; Abhishek Tyagi

doi:10.1080/02664763.2021.1928018

A discrete analogue of odd Weibull-G family of distributions: properties, classical and Bayesian estimation with applications to count data

J Appl Stat. 2021 May 24;49(11):2928-2952. doi: 10.1080/02664763.2021.1928018. eCollection 2022.

Authors

M El-Morshedy^{1

2}, M S Eliwa², Abhishek Tyagi³

Affiliations

¹ Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, Saudi Arabia.
² Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt.
³ Department of Statistics, Chaudhary Charan Singh University, Meerut, India.

Abstract

In the statistical literature, several discrete distributions have been developed so far. However, in this progressive technological era, the data generated from different fields is getting complicated day by day, making it difficult to analyze this real data through the various discrete distributions available in the existing literature. In this context, we have proposed a new flexible family of discrete models named discrete odd Weibull-G (DOW-G) family. Its several impressive distributional characteristics are derived. A key feature of the proposed family is its failure rate function that can take a variety of shapes for distinct values of the unknown parameters, like decreasing, increasing, constant, J-, and bathtub-shaped. Furthermore, the presented family not only adequately captures the skewed and symmetric data sets, but it can also provide a better fit to equi-, over-, under-dispersed data. After producing the general class, two particular distributions of the DOW-G family are extensively studied. The parameters estimation of the proposed family, are explored by the method of maximum likelihood and Bayesian approach. A compact Monte Carlo simulation study is performed to assess the behavior of the estimation methods. Finally, we have explained the usefulness of the proposed family by using two different real data sets.

Keywords: 62E15; 62F10; 62F15; Bayesian method; Discrete distributions; L-moment statistics; dispersion index; maximum likelihood method; odd Weibull-G family; simulation.