Progressive censoring schemes for marshall-olkin pareto distribution with applications: Estimation and prediction

Abstract

In this paper two prediction methods are used to predict the non-observed (censored) units under progressive Type-II censored samples. The lifetimes of the units follow Marshall-Olkin Pareto distribution. We observe the posterior predictive density of the non-observed units and construct predictive intervals as well. Furthermore, we provide inference on the unknown parameters of the Marshall-Olkin model, so we observe point and interval estimation by using maximum likelihood and Bayesian estimation methods. Bayes estimation methods are obtained under quadratic loss function. EM algorithm is used to obtain numerical values of the Maximum likelihood method and Gibbs and the Monte Carlo Markov chain techniques are utilized for Bayesian calculations. A simulation study is performed to evaluate the performance of the estimators with respect to the mean square errors and the biases. Finally, we find the best prediction method by implementing a real data example under progressive Type-II censoring schemes.

Bayes Estimation For The Rayleigh Weibull Distribution Based On Progressive Type-II Censored Samples For Cancer Data In Medicine

“…Aljuaid [15], Ahmed [16], Singh et al [17], Liao ang Gui [18], Abbas et al [19], Sultan et al [20], Alshenawy [21], Mukhtar [22], Wu and Gui [23] ,Almongy et al [24], Qiao and Gui [25], Wu [26], El-Morshedy et al [27], El-Sherpieny et al [28], Liang et al [29], Alshenawy et al [30], Almetwally et al [31], Muhammed and Almetwally [32]).…”

Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine

“…There are a lot of studies that refer to the parameter estimation of different distributions under PTR-II censored samples (Ali Mousa [17], Balakrishnan [18], Ali Mousa and Al-Sagheer [19], Wu et al [20], Panahi and Asadi [21], Aljuaid [22], Ahmed [23], Singh et al [24], Liao ang Gui [25], Abbas et al [26], Sultan et al [27], Alshenawy [28], Mukhtar [29], Wu and Gui [30], Almongy et al [31], Qiao and Gui [32], Wu [33], El-Morshedy et al [34], El-Sherpieny et al [35], Liang et al [36], Alshenawy et al [37], Almetwally et al [38], Muhammed and Almetwally [39], Çiftci et al [40]). Based on the above studies, the main purpose of this study is to obtain the approximate Bayes estimators under the square error loss functions and then to check them with maximum likelihood estimators (MLEs) in the aspect of the estimated risk (ER).…”