Non-linear failure rate: A Bayes study using Hamiltonian Monte Carlo simulation

Abstract

A generalization of the linear failure rate called non-linear failure rate is introduced, analyzed, and applied to real data sets for both censored and uncensored data. The Hamiltonian Monte Carlo and cross-entropy methods have been exploited to empower the traditional methods of statistical estimation. We have obtained the Bayes estimators of parameters and reliability characteristics using Hamiltonian Monte Carlo and these estimators are considered under both symmetric and asymmetric loss functions. Additionally, the maximum likelihood estimators of parameters are obtained by using the cross-entropy method to optimize the log-likelihood function. The superiority of the proposed model and estimation procedures are demonstrated on real data sets adopted from references.