Classical and Bayesian Estimation for a New Long Tailed Distribution: Modi-Lomax Distribution

Abstract

This paper presents the new Modi-Lomax distribution (MOLD), a three-parameter distribution obtained by using the Modi family generator to include one extra shape parameter in the standard two-parameter Lomax distribution. We establish extensive statistical properties such as survival function, hazard rate function, moment generating function, quantile function with quartile representations, mean residual lifetime, order statistics, and stress-strength reliability. For parameter estimation, we use maximum likelihood estimation and Bayesian methods with Gamma priors under squared error loss functions, comparing their performances based on bias and mean square error criteria. The practical usefulness of MOLD is shown through the analysis of one real data set of bladder cancer patients and a comparative analysis with a number of alternative distributions. Results validate the superior flexibility and goodness-of-fit of the suggested distribution under different test criteria, emphasizing its flexibility to model data with diverse failure rate shapes and aging behaviours. This paper makes MOLD a great contribution to lifetime distributions with prominent practice in reliability engineering and survival analysis.