• 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.20 no.6
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• pp.1199-1206
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• 2009

This paper deals with the estimation based on progressive Type-II censored samples from the double Rayleigh distribution. We derive some estimators of the location and scale parameters of the double Rayleigh distribution based on progressive 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 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.21 no.2
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• pp.317-325
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• 2010

In this paper, we develop four modified empirical distribution function (EDF) type tests using approximate maximum likelihood estimators for the half-logistic distribution based on multiply Type-II censored samples. We also propose modified normalize sample Lorenz curve polt and new test statistics. We compare the above test statistics in the sense of the power for various censored samples. We present an example to illustrate this method.

• International Journal of Reliability and Applications
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• v.7 no.2
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• pp.187-201
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• 2006

In this paper, we derive recurrence relations for the single and product moments of progressively Type-II right censored order statistics from half logistic distribution. Next, we derive the maximum likelihood estimators (MLEs) of the location and scale parameters of the half logistic distribution. In addition, we use the setup proposed by Balakrishnan and Aggarwala (2000) to compute the approximate best linear unbiased estimates (ABLUEs) of the location and scale parameters. Finally, we point out a simulation study to compare between the efficiency of the techniques considered for the estimation.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.697-704
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• 2012

The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The $AMLE_{II}$ is better than MLE and $AMLE_I$ in the sense of the MSE.

• 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.

• Communications for Statistical Applications and Methods
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• v.4 no.3
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• pp.929-941
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• 1997

In this paper, we propose the minimum risk estimator (MRE) and the approximate maximum likelihood estimator (AMLE) of the location and the scale parameters of the two-parameter exponential distribution with Type-II censoring. The MRE's can be derived by minimizing the mean squared error among the class of estimators which include some estimators as special cases. We show that the MRE's are more efficient than the other estimators of the scale and the location parameter in the terms of the mean squared error.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.329-344
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• 2007

In this paper, we shall propose the AMLEs of the scale parameter and the location parameter in the two-parameter Rayleigh distribution based on progressive Type-II censored samples when one parameter is known. We also propose the AMLEs of the two parameters in the Rayleigh distribution based on progressive Type-II censored samples when two parameters are unknown. We simulate the mean squared errors of the proposed estimators through Monte Carlo simulation for various censoring schemes.

• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.29-41
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• 2017

The estimation problem of expected time to failure of units is studied in a discrete set up. A simple step-stress accelerated life testing is considered with a Type-I censored sample from geometric distribution that is a commonly used distribution to model the lifetime of a device in discrete case. Maximum likelihood estimators as well as the associated distributions are derived. Exact, approximate and bootstrap approaches construct confidence intervals that are compared via a simulation study. Optimal confidence intervals are suggested in view of the expected width and coverage probability criteria. An illustrative example is also presented to explain the results of the paper. Finally, some conclusions are stated.