Estimation of the inverted exponentiated Rayleigh Distribution Based on Adaptive Type II Progressive Hybrid Censored Sample

Abstract

In this paper, the problem of estimating parameters of the inverted exponentiated Rayleigh distribution under adaptive Type II progressive hybrid censored sample is discussed. The maximum likelihood estimators (MLEs) are developed for estimating the unknown parameters. The asymptotic normality of the MLEs is used to construct the approximate confidence intervals for the parameters. By applying the Bayesian approach, the estimators of the unknown parameters are derived under symmetric and asymmetric loss functions. The Bayesian estimates are evaluated by using the Lindley’s approximation as well as the Monte Carlo Markov chain (MCMC) technique together with Metropolis–Hastings algorithm. The MCMC samples are further utilized to construct the Bayesian intervals for the unknown parameters. Monte Carlo simulations are implemented and observations are given. Finally, the data of the maximum spreading diameter of nano-droplet impact on hydrophobic surfaces is analyzed to illustrative purposes.