Author(s)

Tahani A. Abushal¹, Areej M. AL-Zaydi²

¹Department of Mathematics, Umm AL-Qura University, Mecca, KSA.
²Department of Mathematics, Taif University, Taif, KSA.

The main purpose of this paper is to obtain the inference of parameters of heterogeneous population represented by finite mixture of two Pareto (MTP) distributions of the second kind. The constant-partially accelerated life tests are applied based on progressively type-II censored samples. The maximum likelihood estimates (MLEs) for the considered parameters are obtained by solving the likelihood equations of the model parameters numerically. The Bayes estimators are obtained by using Markov chain Monte Carlo algorithm under the balanced squared error loss function. Based on Monte Carlo simulation, Bayes estimators are compared with their corresponding maximum likelihood estimators. The two-sample prediction technique is considered to derive Bayesian prediction bounds for future order statistics based on progressively type-II censored informative samples obtained from constant-partially accelerated life testing models. The informative and future samples are assumed to be obtained from the same population. The coverage probabilities and the average interval lengths of the confidence intervals are computed via a Monte Carlo simulation to investigate the procedure of the prediction intervals. Analysis of a simulated data set has also been presented for illustrative purposes. Finally, comparisons are made between Bayesian and maximum likelihood estimators via a Monte Carlo simulation study.

Pareto Distribution, Finite Mixtures, Constant—Partially ALT, Progressive Type-II Censoring, Bayesian Estimation, Maximum Likelihood Estimation, Bayesian Prediction, the Two-Sample Prediction, MCMC

Abushal, T. and AL-Zaydi, A. (2017) Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring. Open Journal of Statistics, 7, 323-346. doi: 10.4236/ojs.2017.72024.