• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.413-430
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• 2020

The multiply Type-II hybrid censoring scheme is disadvantaged by an experiment time that is too long. To overcome this limitation, we propose a generalized multiply Type-II hybrid censoring scheme. Some estimators of the scale parameter of the exponential distribution are derived under a generalized multiply Type-II hybrid censoring scheme. First, the maximum likelihood estimator of the scale parameter of the exponential distribution is obtained under the proposed censoring scheme. Second, we obtain the Bayes estimators under different loss functions with a noninformative prior and an informative prior. We approximate the Bayes estimators by Lindleys approximation and the Tierney-Kadane method since the posterior distributions obtained by the two priors are complicated. In addition, the Bayes estimators are obtained by using the Markov Chain Monte Carlo samples. Finally, all proposed estimators are compared in the sense of the mean squared error through the Monte Carlo simulation and applied to real data.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• Journal of the Korean Data and Information Science Society
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• v.20 no.4
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• pp.719-731
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• 2009

This paper deals with properties of the exponentiated extreme value distribution. We derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponentiated extreme value distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.603-606
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• 2003

The maximum likelihood estimators of the eigenvalues and eigenvectors of $$\Sigma$$_1$^{-1}$$\Sigma$$_2$are shown to be the eigenvalues and eigenvectors of $S$_1$^{1}$S$_2$ under multivariate normality and are explicitly derived. The nature of the eigenvalues and eigenvectors of $$\Sigma$$_1$^{-1}$$\Sigma$$_2$ or their estimators will be uncovered.

• 한국데이터정보과학회:학술대회논문집
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• 2005.04a
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• pp.59-68
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• 2005

We consider the problem of estimating the scale and shape parameter of the Weibull distribution based on censored samples. we propose the approximate maximum likelihood estimators (AMLEs) of the scale and shape parameters in the Weibull distribution based on Type-II censored samples. We compare the proposed estimators in the sense of mean squared error (MSE).

• Journal of the Korean Data and Information Science Society
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• v.16 no.3
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• pp.629-638
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• 2005

We derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the extreme value distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.1-18
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• 1995

The generalized logit model of nominal type with random regressors is studied for bootstrapping. In particular, asymptotic normality and consistency of bootstrap model estimators are derived. It is shown that the bootstrap approximation to the distribution of the maximum likelihood estimators is valid for alsomt all sample sequences.

• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.1
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• pp.1-15
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• 1989

Multistate survival data with censoring often arise in biomedical experiments. In particular, a four-state space is used for cancer clinical trials. In a four-state space, each patient may either respond to a given treatment and then relapse or may progress without responding. In this four-state space, a model which combines the Markov and semi-Markov models is proposed. In this combined model, the generalized maximum likelihood estimators of the Markov and semi-Markov hazard functions are derived. These estimators are illustrated for the data collected in a study of treatments for advanced breast cancer.

• Journal of the Korean Data and Information Science Society
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• v.6 no.2
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• pp.77-83
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• 1995

The inferences on a series system under the usual condition using data from constant stress partially accelerated life tests and type I censoring is studied. Two optimal designs to determine the sample proportion allocated each stress level model are also presented, which minimize the sum of the generalized asymptotic variances of maximum likelihood estimators of the failure rate and the acceleration factors and the sum of the asymptotic variances of maximum likelihood estimators of the acceleration factors for each component. Each component of a system is assumed to follow an exponenial distribution.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1107-1117
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• 2005

We consider the problem of estimating the scale and shape parameters in the Weibull distribution based on censored samples. We propose the approximate maximum likelihood estimators (AMLEs) of the scale and shape parameters in the Weibull distribution based on Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error (MSE).