• 한국데이터정보과학회:학술대회논문집
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• 2003.10a
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• pp.13-18
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• 2003

When the available sample is multiply type-II censored, the maximum likelihood estimators of the location and scale parameters of two- parameter exponential distribution do not exist explicitly. In this case, we propose several approximate maximum likelihood estimators by approximating the likelihood equations appropriately. We present an example to illustrate these estimation methods.

• Journal of the Korean Data and Information Science Society
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• v.18 no.4
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• pp.1081-1091
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• 2007

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter in an exponentiated logistic 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. We also propose and compare the estimators of the reliability function by using the proposed estimators of the parameters.

• Communications for Statistical Applications and Methods
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• v.12 no.3
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• pp.643-652
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• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also 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.20 no.5
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• pp.405-416
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• 2013

This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.573-584
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• 2007

We define a skew-symmetric Laplace distribution by a symmetric Laplace distribution and evaluate its coefficient of skewness. And we derive an approximate maximum likelihood estimator(AME) and a moment estimator(MME) of a skewed parameter in a skew-symmetric Laplace distribution, and hence compare simulated mean squared errors of those estimators. We compare asymptotic mean squared errors of two defined estimators of reliability in two independent skew-symmetric distributions.

• Journal of the Korean Data and Information Science Society
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• v.10 no.2
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• pp.405-413
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• 1999

By assuming a type-II censoring, we propose the approximate maximum likelihood estimators (AMLEs) of the location and the scale parameters of the two-parameter Rayleigh distribution and calculate the asymptotic variances and covariance of the AMLEs.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1441-1448
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• 2008

We propose the modified quantile-quantile (Q-Q) plot using the approximate maximum likelihood estimators and the modified normalized sample Lorenz curve (NSLC) plot for the extreme value distribution based on multiply Type-II censored samples. Using two example data sets, we picture the modified Q-Q plot and the modified NSLC plot.

• 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.1 no.1
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• pp.10-19
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• 1994

We study the change-point problem in the context of system reliability models. The maximum likelihood estimators are obtained based on the Jelinski and Moranda model. To find the approximate distribution of the change-point estimator, we suggest of parametric bootstrap method in which the estimators are substituted in the assumed model. Through an example we illustrate the proposed method.

• 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.