• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.

• Journal of the Korean Data and Information Science Society
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• v.25 no.1
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• pp.195-209
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• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2006.04a
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• pp.279-293
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• 2006

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponential distribution based on multiply Type-II censored samples. Then three type tests, including the modified Clamor-von Mises test, the modified Watson test and the modified Kolmogorov-Smirnov test are developed for the exponential distribution based on multiply Type-II censored samples by using the proposed estimators. For each test, Monte Carlo techniques are used to generate critical values. The powers of these tests are investigated under several alternative distributions.

• 한국데이터정보과학회:학술대회논문집
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• 2002.06a
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• pp.89-95
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• 2002

This paper considers the problem of estimating paramaters of the bivariate exponential distribution with a loaction parameter for a two-component shared parallel system using component data from system-level life test terminated at the time of the prespecified number of system failure. In the system-level life testing, there are three patterns of failure types; 1) both component failed 2) both component censored 3) one is failed and the other is censored. In the third case, we assume that the failure time might be known or unknown. The maximum likelihood estimators are obtained for the case of known/unknown failure time when the other component is censored.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.255-266
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• 2007

A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.

• Wind and Structures
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• v.26 no.6
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• pp.383-395
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• 2018

An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.243-250
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• 2002

This paper considers the problem of estimating parameters of the bivariate exponential distribution with a location parameter for a two-component shared parallel system using component data from system-level life test terminated at the time of the prespecified number of system failure. In the system-level life testing, there are three patterns of failure types ; 1) both component failed 2) both component censored 3) one is failed and the other is censored. In the third case, we assume that the failure time might be known or unknown. The maximum likelihood estimators are obtained for the case of known/unknown failure time when the other component is censored.

• Communications for Statistical Applications and Methods
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• v.20 no.4
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• pp.321-327
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• 2013

Bayesian and empirical Bayesian methods have become quite popular in the theory and practice of statistics. However, the objective is to often produce an ensemble of parameter estimates as well as to produce the histogram of the estimates. For example, in insurance pricing, the accurate point estimates of risk for each group is necessary and also proper dispersion estimation should be considered. Well-known Bayes estimates (which is the posterior means under quadratic loss) are underdispersed as an estimate of the histogram of parameters. The adjustment of Bayes estimates to correct this problem is known as constrained Bayes estimators, which are matching the first two empirical moments. In this paper, we propose a way to apply the constrained Bayes estimators in insurance pricing, which is required to estimate accurately both location and dispersion. Also, the benefit of the constrained Bayes estimates will be discussed by analyzing real insurance accident data.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1581-1589
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• 2014

In this paper, we consider maximum likelihood estimators of the location and scale parameters for the half-logistic distribution when samples are multiply Type I hybrid censored. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($\hat{\sigma}_I$, $\hat{\sigma}_{II}$). We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The approximate MLE of the second type is better than that of the first type in the sense of the RMSE. Further an illustrative example with the real data is presented.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.