Entropy Bayesian Estimation for Lomax Distribution Based on Record

Abstract

In this paper, estimation of entropy for Lomax distribution based on upper record values is considered. Bayesian estimator of Shannon entropy is discussed under informative and non-informative priors. The entropy Bayesian estimator and the corresponding credible interval on the basis of a linear exponential, squared error and precautionary loss functions are derived. The Metropolis-Hastings algorithm is used to generate random variables. Monte Carlo simulations based on Gibbs sampling are conducted to implement the accuracy of estimates for different number of records.  Real data example is analyzed for illustration purposes. In general, based on the outcomes of study, the Bayesian estimates of entropy tend to the true value as the number of record increases. Further, Bayesian estimate of entropy under LINEX loss function is preferable than the other estimates in most of situations.