Estimation and prediction using classical and Bayesian approaches for Burr III model under progressive type-I hybrid censoring

Abstract

In this paper we address the problems of estimation and prediction when lifetime data following Burr type III distribution are observed under progressive type-I hybrid censoring. We first obtain maximum likelihood estimators of unknown parameters using expectation maximization and stochastic expectation maximization algorithms, and associated interval estimates using Fisher information matrix. We then obtain Bayes estimators based on non-informative and informative priors under squared error, entropy and Linex loss functions using the method of Tierney-Kadane and importance sampling technique, and associated highest posterior density interval estimates by making use of Chen and Shao method. We further predict the censored observations and interval estimates under classical and Bayesian approaches. Finally we analyze two real data sets, and conduct a simulation study to compare the performance of various proposed estimators and predictors.

Discriminating among inverse Weibull, lognormal, and inverse Gaussian distributions

“…The idea of SEM algorithm is to replace the censored observations with simulated observations generated from the conditional distribution given the observed data. In many problems, the SEM approach has been found to be computationally simpler and more suitable than the EM algorithm, see Zhang et al., 24 Arabi Belaghi et al., 25 Singh et al., 26 and Mohammadi Monfared et al 27 . We apply the same idea here, and generate the independent censored lifetimes, say $$Z = (Z_{1}, Z_{2}, \ldots, Z_{n-r})$$ from the conditional distribution function given by $$ (F(Z_i; \theta)-F(t; \theta))/(1-F(t; \theta)), Z_i > t$$.…”

Prediction of future failures in the log-logistic distribution based on hybrid censored data

“…The one and two sample Bayesian prediction problems with hybrid censored data were considered by Shafay et al (2012). Classical and Bayesian prediction in the Bur III model were discussed by Singh et al (2019). ChauPattnaik et al (2021) discuss component based reliability prediction using Markov chains techniques.…”

Prediction of Kumaraswamy distribution in constant‐stress model based on type‐I hybrid censored data

“…See, for example, Kundu and Park and Balakrishnan . Prediction based on censoring schemes has been discussed by several authors, including, Shafay and Balakrishnan , Panahi and Sayyareh , Asgharzadeh et al , Arabi Belaghi et al , and Asl et al and Singh et al .…”