Dynamic cumulative residual Renyi entropy for Lomax distribution: Bayesian and non-Bayesian methods

An alternative measure of uncertainty related to residual lifetime function is the dynamic cumulative residual entropy which plays a significant role in reliability and survival analysis. This article deals with estimating dynamic cumulative residual Renyi entropy (DCRRE) for Lomax distribution using maximum likelihood and Bayesian methods of estimation. The maximum likelihood estimates and approximate confidence intervals of DCRRE are derived. Bayesian estimates and Bayesian credible intervals are derived based on gamma priors for the DCRRE under squared error, linear exponential (LINEX) and precautionary loss functions. The Metropolis Hastings algorithm is employed to generate Markov chain Monte Carlo samples from the posterior distributions. The Bayes estimates are compared through Monte Carlo simulations. Regarding simulation results, we observe that the maximum likelihood and Bayesian estimates of the DCRRE are decreasing function on time. Further, maximum likelihood and Bayesian estimates of the DCRRE perform well as the sample size increases. Bayesian estimate of the DCRRE under LINEX loss function is more convenient than the other estimates in the most of the situations. Real data set is analyzed for clarifying purposes.

Automated summary

This article discusses estimating dynamic cumulative residual Renyi entropy (DCRRE) for Lomax distribution using maximum likelihood and Bayesian methods, and compares the results using Monte Carlo simulations. It is found that DCRRE estimates decrease over time and perform well with increasing sample size, with Bayesian estimates under LINEX loss function being more convenient in most situations. Real data set analysis is conducted for further clarification.