Inference for exponentiated Pareto distribution based on progressive first-failure censored data with application to cumin essential oil data

Abstract

The purpose of this article is to consider the statistical inference of the unknown parameters of an exponentiated Pareto (EP) distribution and examine its suitability in modeling the main component of cumin essential oil data under progressive first-failure censoring scheme. Since the maximum likelihood estimators of the parameters cannot be obtained in nice closed forms, we suggest an EM algorithm to compute them. The Bayes estimates are computed using the Lindley’s approximation as well as Markov Chain Monte Carlo (MCMC) technique. Samples generated from the MCMC technique are further used for constructing highest posterior density intervals for unknown parameters. Monte Carlo simulations are performed to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, the suitability of the EP distribution in modeling the cumin essential oil data is examined. The results suggest that the EP distribution can be considered as an adequate model for this data.