Journal of the Iranian Statistical Society

Estimation for the Three-Parameter Exponentiated Weibull Distribution under Progressive Censored Dat

Document Type : Original Article

Authors

1 Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Iran.

2 Department of Mathematics and Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.

Abstract

In this paper, we consider the problem of estimating the unknown parameters of an exponentiated Weibull distribution when the data are observed in the presence of progressively Type II censoring. We observed that the maximum likelihood estimators do not have a closed form, and so require a numerical technique to compute, further the implementation of the EM algorithm still requires the numerical techniques. So we employ the stochastic expectation-maximization (SEM) algorithm to estimate the model parameters and further to construct the associated asymptotic confidence intervals of the unknown parameters. Moreover, under Bayesian approach, we consider symmetric and asymmetric loss functions and compute the Bayesian estimates using the Lindley’s approximation and Gibbs sampler together with Metropolis Hastings algorithm. The highest posterior density (HPD) credible intervals are also constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, a real life example is considered to illustrate the application and development of the inference methods.

Keywords

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Journal of the Iranian Statistical Society
Volume 21, Issue 1
June 2022
Pages 153-177
  • Receive Date: 04 November 2020
  • Revise Date: 17 December 2021
  • Accept Date: 19 May 2022