One- and Two-Sample Bayesian Prediction Intervals Based on Type-I Hybrid Censored Data

Abstract

In this article, we consider a general form for the underlying distribution and a general conjugate prior, and describe a general procedure for determining the Bayesian prediction intervals for future lifetimes based on an observed Type-I hybrid censored data. For the illustration of the developed results, the Exponential( ) and Pareto( ) distributions are used as examples. One-sample Bayesian predictive survival function can not be obtained in closed-form and so Gibbs sampling procedure is used to draw Markov Chain Monte Carlo (MCMC) samples, which are then used to compute the approximate predictive survival function. Finally, some numerical results are presented to illustrate all the inferential results developed here.

Parametric inference of non-informative censored time-to-event data

“…Syuan-Rong and Shuo-Jye 7 also considered Bayesian estimation and prediction for Weibull model with progressive censoring. Similar work can be seen in Shafay and Balakrishnan 8 , who studied one-and two-sample Bayesian prediction intervals based on type-I hybrid censored data. Gupta and Kundu 9 studied generalized exponential distributions with different methods of estimation, see also Refs.…”

“…Example 1 In this section, we analyse one data set to obtain the parameter estimates and their standard errors in order to compare the estimators assumed in this paper. The data below are obtained from Lawless 20 about remission times, in weeks, for a group of 30 patients with leukaemia who received similar treatment (asterisks denote censoring times): 1,1,2,4,4,6,6,6,7,8,9,9,10,12,13,14,18,19,24,26,29, 31*, 42, 45*, 50*, 57, 60, 71*, 85*, 91. Using the iterative procedure suggested from the beginning of this paper, the MLEs ofθ andp can be obtained as 28.27991 and 0.99201, respectively, with their corresponding standard errors as 1.56748 and 0.02386.…”

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 .…”

Statistical Inference and Prediction for the Gompertz Distribution Based on Multiply Type-I Censored Data

“…Prediction intervals were discussed by many authors, examples of these papers are as follows: Mohie El-Din and Shafay [5], obtained the Bayesian prediction intervals depending on progressively Type-II censored data. Also Bayesian prediction intervals based on the Type-I hybrid censored data were studied by Shafay and Balakrishnan [6]. Mohie El-Din et al [7] studied the Bayesian prediction intervals of generalized order statistics based on multiply Type-II censored data.…”