Topp–Leone Poisson Exponential Distribution: A Classical and Bayesian Approach

Abstract

In this paper, we propose a new three-parameter lifetime distribution, which has increasing, decreasing and constant failure rate. The new distribution can be use on a latent complementary risk scenario. The properties of the proposed distribution are discussed, including a formal proof of its density function and an explicit algebraic formula for its quantiles, skewness, kurtosis, survival and hazard functions. Also, we have been discussed inference aspects of the model proposed via Bayesian inference by using Markov chain Monte Carlo simulation. A simulation study performed in order to investigate the classical, Bayesian properties of the proposed estimators obtained under the assumptions of non-informative priors. Further, the applicability of proposed distribution is illustrated on a real data set. © 2023, The Indian Society for Probability and Statistics (ISPS).