Discrete additive Perks–Weibull distribution: properties and applications

Abstract

In this study, we introduce a discrete version of continuous additive Perks–Weibull distribution proposed by Singh (Commun Math Stat 4(4):473–493, 2016), and named as discrete additive Perks–Weibull distribution. This proposed distribution has bathtub-shaped as well as increasing hazard rate, and due to this characteristic it lies in the class of few discrete models exhibit bathtub-shaped hazard rate. We have discussed some important distributional properties including moment generating function, probability generating function, moments, cumulative distribution function, quantile function, order statistics, infinite divisibility and some reliability properties such as survival function, hazard rate function and stress–strength reliability. In classical scenario, the parameters of the proposed distribution are estimated by using method of maximum likelihood, whereas in Bayesian approach, we assume joint prior as Dirichlet Type-II distribution for the estimation of parameters involved in the model. A simulation study is performed to compare the performance of different estimation methods. Finally, the model applications are demonstrated by using three real datasets.