• 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.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.20 no.5
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• pp.347-356
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• 2013

We propose a sequential method to construct approximate confidence limits for the ratio of two independent sequences of binomial variates with unequal sample sizes. Due to the nonexistence of an unbiased estimator for the ratio, we develop the procedure based on a modified maximum likelihood estimator (MLE). We generalize the results of Cho and Govindarajulu (2008) by defining the sample-ratio when sample sizes are not equal. In addition, we investigate the large-sample properties of the proposed estimator and its finite sample behavior through numerical studies, and we make comparisons from the sample information view points.

• 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.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1125-1145
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• 2010

For modeling(skewed) semicircular data, we derive a new exponential family of distributions. We extend it to the l-axial exponential family of distributions by a projection for modeling any arc of arbitrary length. It is straightforward to generate samples from the l-axial exponential family of distributions. Asymptotic result reveals that the linear exponential family of distributions can be used to approximate the l-axial exponential family of distributions. Some trigonometric moments are also derived in closed forms. The maximum likelihood estimation is adopted to estimate model parameters. Some hypotheses tests and confidence intervals are also developed. The Kolmogorov-Smirnov test is adopted for a goodness of t test of the l-axial exponential family of distributions. Samples of orientations are used to demonstrate the proposed model.

• Journal of the Korean Statistical Society
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• v.15 no.2
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• pp.97-106
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• 1986

Assume that $X_1, X_2, \cdots, X_N$ are iid p-dimensional normal random vectors ($p \geq 3$) with unknown covariance matrix. The problem of estimating multivariate normal mean vector in an empirical Bayes situation is considered. Empirical Bayes estimators, obtained by Bayes treatmetn of the covariance matrix, are presented. It is shown that the estimators are minimax, each of which domainates teh maximum likelihood estimator (MLE), when the loss is nonsingular quadratic loss. We also derive approximate credibility region for the mean vector that takes advantage of the fact that the MLE is not the best estimator.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.901-909
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• 2013

A skewed double power function distribution is defined by a double power function distribution. We shall evaluate the coefficient of the skewness of a skewed double power function distribution. We shall obtain an approximate maximum likelihood estimator (MLE) and a moment estimator (MME) of the skew parameter in the skewed double power function distribution, and compare simulated mean squared errors for those estimators. And we shall compare simulated MSEs of two proposed reliability estimators in two independent skewed double power function distributions with different skew parameters.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1249-1257
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• 2012

In this paper, we derive maximum likelihood estimators (MLEs) and approximate MLEs (AMLEs) of the unknown parameters in a generalized half logistic distribution when the data are upper record values. As an illustration, we examine the validity of our estimation using real data and simulated data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE) through a Monte Carlo simulation for various record values of size.

• 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.