Progressive censoring schemes for marshall-olkin pareto distribution with applications: Estimation and prediction (original) (raw)
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Journal of Mathematics, 2021
This paper describes two prediction methods for predicting the non-observed (censored) units under progressive Type-II censored samples. The lifetimes under consideration are following a new two-parameter Pareto distribution. Furthermore, point and interval estimation of the unknown parameters of the new Pareto model is obtained. Maximum likelihood and Bayesian estimation methods are considered for that purpose. Since Bayes estimators cannot be expressed explicitly, Gibbs and the Markov Chain Monte Carlo techniques are utilized for Bayesian calculation. We use the posterior predictive density of the non-observed units to construct predictive intervals. A simulation study is performed to evaluate the performance of the estimators via mean square errors and biases and to obtain the best prediction method for the censored observation under progressive Type-II censoring scheme for different sample sizes and different censoring schemes.
Journal of Statistical Computation and Simulation, 2018
In this paper, we consider Marshall-Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley's approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate the results derived.
American Journal of Theoretical and Applied Statistics, 2013
In this paper, based on a new type of censoring scheme called a progressive first-failure censored, the maximum likelihood (ML) and the Bayes estimators for the two unknown parameters of the Generalized Pareto (GP) distribution are derived. This type of censoring contains as special cases various types of censoring schemes used in the literature. A Bayesian approach using Markov Chain Monte Carlo (MCMC) method to generate from the posterior distributions and in turn computing the Bayes estimators are developed. Point estimation and confidence intervals based on maximum likelihood and bootstrap methods are also proposed. The approximate Bayes estimators have been obtained under the assumptions of informative and non-informative priors. A numerical example is provided to illustrate the proposed methods. Finally, the maximum likelihood and different Bayes estimators are compared via a Monte Carlo simulation study.
Complexity , 2022
A new three-parameter extension of the generalized-exponential distribution, which has various hazard rates that can be increasing, decreasing, bathtub, or inverted tub, known as the Marshall-Olkin generalized-exponential (MOGE) distribution has been considered. So, this article addresses the problem of estimating the unknown parameters and survival characteristics of the three-parameter MOGE lifetime distribution when the sample is obtained from progressive type-II censoring via maximum likelihood and Bayesian approaches. Making use of the s-normality of classical estimators, two types of approximate confidence intervals are constructed via the observed Fisher information matrix. Using gamma conjugate priors, the Bayes estimators against the squared-error and linear-exponential loss functions are derived. As expected, the Bayes estimates are not explicitly expressed, thus the Markov chain Monte Carlo techniques are implemented to approximate the Bayes point estimates and to construct the associated highest posterior density credible intervals. e performance of proposed estimators is evaluated via some numerical comparisons and some specific recommendations are also made. We further discuss the issue of determining the optimum progressive censoring plan among different competing censoring plans using three optimality criteria. Finally, two real-life datasets are analyzed to demonstrate how the proposed methods can be used in real-life scenarios.
Mathematics, 2018
In this paper, first we consider the maximum likelihood estimators for two unknown parameters, reliability and hazard functions of the generalized Pareto distribution under progressively Type II censored sample. Next, we discuss the asymptotic confidence intervals for two unknown parameters, reliability and hazard functions by using the delta method. Then, based on the bootstrap algorithm, we obtain another two pairs of approximate confidence intervals. Furthermore, by applying the Markov Chain Monte Carlo techniques, we derive the Bayesian estimates of the two unknown parameters, reliability and hazard functions under various balanced loss functions and the corresponding confidence intervals. A simulation study was conducted to compare the performances of the proposed estimators. A real dataset analysis was carried out to illustrate the proposed methods.
Journal of Statistical Theory and Applications, 2018
This paper studies the Bayes estimator, the maximum likelihood estimator and the approximate likelihood estimator of the scale parameter for the Marshall-Olkin exponential distribution under the progressive type-II censored sample. All the estimators, Bayes estimator, maximum likelihood estimator and approximate likelihood estimator are presented and derived in simple forms. It observed that the Bayes estimator and the maximum likelihood estimator can not be solved analytically, hence it is solved numerically. Finally the comparison method is presented in order to compare the performance between these estimators.
Journal of Statistics and Management Systems, 2018
In this paper, we obtain the maximum likelihood, Bayes and parametric bootstrap estimators for the parameters of a new Weibull-Pareto distribution (NWPD) and some lifetime indices such as reliability function S(t), failure rate h(t) function and coefficient of variation CV are obtained. The previous methods are studied in the case of an adaptive Type-II progressive censoring (Ada-T-II-Pro-C). Approximate confidence intervals (ACIs) of the unknown parameters are constructed based on the asymptotic normality of maximum likelihood estimators (MLEs). Bayes estimates and the symmetric credible intervals (CRIs) of the unknown quantities are calculated based on the Gibbs sampler within Metropolis-Hasting (M-H) algorithm procedure. The results of Bayes estimates are obtained under the consideration of the informative prior function with respect to the squared error loss (SEL) function. Two numerical examples are presented to illustrate the proposed methods, one of them is a simulated example and the other is a real life example. Finally, the performance of different Bayes estimates are compared with maximum likelihood (ML) and two parametric bootstrap estimates, through a Monte Carlo simulation study.
Bayesian two-sample prediction with progressively type-II censored data for some lifetime models
Journal of Iranian Statistical Society, 2011
Prediction on the basis of censored data is very important topic in many fields including medical and engineering sciences. In this paper, based on progressive Type-II right censoring scheme, we will discuss Bayesian two-sample prediction. A general form for lifetime model including some well known and useful models such as Weibull and Pareto is considered for obtaining prediction bounds as well as Bayes predictive estimations under squared error loss function for the s th order statistic in a future random sample drawn from the parent population, independently and with an arbitrary progressive censoring scheme. As an illustration, we will present two numerical examples as well as a simulation study to carry out the performance of the procedures obtained.
Computational Statistics & Data Analysis, 2002
This paper presents Bayesian estimation of the survival function of the Pareto distribution of the second kind using the methods of and . A numerical example is given to illustrate the results derived. Based on a Monte Carlo simulation study, comparisons are made between these two methods, as well as, their competitor, the maximum likelihood method, by considering di erent censored samples and several values of the true shape and scale parameters.
Journal of Statistical Research of Iran, 2016
Prediction on the basis of censored data is very important topic in many fields including medical and engineering sciences. In this paper, based on progressive Type-II right censoring scheme, we will discuss Bayesian two-sample prediction. A general form for lifetime model including some well known and useful models such as Weibull and Pareto is considered for obtaining prediction bounds as well as Bayes predictive estimations under squared error loss function for the s th order statistic in a future random sample drawn from the parent population, independently and with an arbitrary progressive censoring scheme. As an illustration, we will present two numerical examples as well as a simulation study to carry out the performance of the procedures obtained.