• Journal of the Korean Data and Information Science Society
• /
• v.21 no.5
• /
• pp.927-934
• /
• 2010

In this paper, we introduce a method of parameter estimation of progressive Type I interval censored sample and progressive type II censored sample. We propose a new parameter estimation method, that is converting the data which obtained by progressive type I interval censored, those data be used to estimate of the parameter in progressive type II censored sample. We used exponential distribution with unknown scale parameter, the maximum likelihood estimator of the parameter calculates from the two methods. A simulation is conducted to compare two kinds of methods, it is found that the proposed method obtains a better estimate than progressive Type I interval censoring method in terms of mean square error.

• Communications for Statistical Applications and Methods
• /
• v.13 no.1
• /
• pp.89-99
• /
• 2006

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

• Communications for Statistical Applications and Methods
• /
• v.23 no.4
• /
• pp.269-285
• /
• 2016

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

• Journal of the Korean Data and Information Science Society
• /
• v.23 no.6
• /
• pp.1271-1277
• /
• 2012

In this paper, we propose an estimation method of the parameter in an exponential distribution based on a progressive Type I interval censored sample with semi-missing observation. The maximum likelihood estimator (MLE) of the parameter in the exponential distribution cannot be obtained explicitly because the intervals are not equal in length under the progressive Type I interval censored sample with semi-missing data. To obtain the MLE of the parameter for the sampling scheme, we propose a method by which progressive Type I interval censored sample with semi-missing data is converted to the progressive Type II interval censored sample. Consequently, the estimation procedures in the progressive Type II interval censored sample can be applied and we obtain the MLE of the parameter and survival function. It will be shown that the obtained estimators have good performance in terms of the mean square error (MSE) and mean integrated square error (MISE).

• Journal of the Korean Data and Information Science Society
• /
• v.24 no.6
• /
• pp.1309-1317
• /
• 2013

There are various parameter estimation methods for the generalized exponential distribution under progressive type I interval censoring. Chen and Lio (2010) studied the parameter estimation method by the maximum likelihood estimation method, mid-point approximation method, expectation maximization algorithm and methods of moments. Among those, mid-point approximation method has the smallest mean square error in the generalized exponential distribution under progressive type I interval censoring. However, this method is difficult to derive closed form of solution for the parameter estimation using by maximum likelihood estimation method. In this paper, we propose two type of approximate maximum likelihood estimate to solve that problem. The simulation results show the obtained estimators have good performance in the sense of the mean square error. And proposed method derive closed form of solution for the parameter estimation from the generalized exponential distribution under progressive type I interval censoring.

• Communications for Statistical Applications and Methods
• /
• v.17 no.1
• /
• pp.99-106
• /
• 2010

In this paper, we present two methods for obtaining prediction intervals for the times to failure of units censored in multiple stages in a progressively censored sample from proportional hazard rate models. A numerical example and a Monte Carlo simulation study are presented to illustrate the prediction methods.