Inference on Constant-Partially Accelerated Life Tests for Mixture of Pareto Distributions under Progressive Type-II Censoring

Abstract

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.

Bayesian Estimation and Prediction Based on Constant Stress-Partially Accelerated Life Testing for Topp Leone-Inverted Kumaraswamy Distribution

“…Combining the LF in (14) and the joint prior distribution given by (16), then the joint posterior distribution for Φ can be obtained as follows:…”

“…Other estimators, such as the least squares estimator may replace the ML estimator. Many authors obtained the Bayes estimators for different other distributions using the symmetric and asymmetric BLF, [see AL-Hussaini and Hussein [22], Al-Zahrani and Al-Sobhi [23], Abushal and AL-Zaydi [16]].…”

“…Assuming that Y ( ) ≤ Y ( ) ≤ ⋯ ≤ Y ( ) are the first r ordered life times in a random sample of n components (Type II censoring) whose failure times are independent and identically distributed as random variables Y`s having the pdf for an item tested at accelerated conditions is given by ( 6) which is an informative sample, and that T ( ) , T ( ) , … , T ( ) is a future independent random sample (of size m) from the same distribution. Our aim is to predict a statistic in the future sample based on the informative sample [see Kaminsky and Rhodin [24], Valiollahi et al [25], Abushal and AL-Zaydi [16], Ateya and Mohammed [26] and Raqab et al [27]].…”

“…Recently many authors have studied PALT from the Bayesian view point, such as Jaheen et al [15] and EL-Sagheer [10]. Also, few studies have considered prediction assuming PALT such as Abushal and AL-Zaydi [16] and Prakash and Singh [17].…”

Evidential Estimation of an Uncertain Mixed Exponential Distribution under Progressive Censoring

“…Tahir et al [ 21 ] studied the problem of estimating the parameters of a three-component mixture of exponential, Rayleigh and Burr Type-XII distributions using the Type-I right censoring scheme in the Bayesian framework. The maximum likelihood and Bayesian estimators of the parameters of a heterogeneous population represented by a finite mixture of two Pareto distributions were discussed in [ 22 ]. Feroze and Aslam [ 23 ] introduced the Bayesian approach for estimating the parameters of the two-component mixture of Weibull distribution under doubly censored samples.…”