• Communications for Statistical Applications and Methods
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• 제3권3호
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• pp.291-297
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• 1996

In this paper, we propose the jackknife estimator and the bootstrap estimator of Gini index of the two-parameter exponential distribution when the location parameter $\theta$ is unknown and the scale parameter $\sigma$is known. Sinilarly, we propose the bias location parameter $\theta$ and the scale parameter $\sigma$ are unknown. The bootstrap estimator is more efficient than the other estimators when the location parameter $\theta$is unknown and the scale parameter $\sigma$ is known, and the bias corrected estimator is more efficient than the MLE when both the location parameter $\theta$ and the scale parameter $\sigma$are unknown.

• Transactions of the Korean Society of Mechanical Engineers A
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• 제33권4호
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• pp.346-352
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• 2009

In the present study, the Weibull statistical analysis using the Monte-Carlo simulation has been performed to investigate the micro-Vickers hardness measurement reliability considering the variability. Experimental indentation test were performed with a micro-Vickers hardness tester for as-received and quenching and tempering specimens in SCM440 steels. The distribution of micro-Vickers hardness is found to be 2-parameter Weibull distribution function. The mean values and coefficients of variation (COV) for both data set are compared with results based on Weibull statistical analysis. Finally, Monte-Carlo simulation was performed in order to evaluate the effect of sample size on the micro-Vickers hardness measurement reliability. For the parent distribution with shape parameter 30.0 and scale parameter 200.0 (COV=0.040), the number of sample data required to obtain the true Weibull parameters was founded by 20. For the parent distribution with shape parameter 10.0 and scale parameter 200.0 (COV=0.1240), the number of sample data required to obtain the true Weibull parameters was founded by 30.

• Journal of the Korean Statistical Society
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• 제23권2호
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• pp.271-292
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• 1994

The comparison of statistical experiments with a common parameter and parameter space is discussed using the concept of the Blackwell's sufficiency and the Shannon's entropy. Binomial and censored experiments are considered as applications. The loss of information is studied under teh aggregated experiments and truncated experiments, and summerized in some tables which make it possible to indicate the choice of an appropriate experiment.

• Communications for Statistical Applications and Methods
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• 제14권1호
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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.

• Journal of Power System Engineering
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• 제14권4호
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• pp.56-62
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• 2010

This paper is concerned with the stochastic nature of elevated temperature tensile strength and creep rupture time in 18Cr-8Ni stainless steels. The Weibull statistical analysis using the NRIM data sheet has been performed to investigate the effects of variability of the elevated temperature tensile strength and creep rupture time on the testing temperature. From those investigations, the distributions of temperature tensile strength and creep rupture time were well followed in 2-parameter Weibull. The shape parameter and scale parameter for the Weibull distribution of tensile strength were decreased with increasing the testing temperature. For the creep rupture time, generally, the shape parameter were decreased with increasing the testing temperature.

• Communications for Statistical Applications and Methods
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• 제24권1호
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• pp.15-27
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• 2017

This paper introduces a two-parameter discrete distribution based on a continuous two-parameter bathtub distribution. It is the only two-parameter discrete distribution that shows a bathtub-shaped hazard function. Some statistical properties of the distribution are discussed. Three different methods are used to estimate its two unknown parameters. The point estimators of the parameters have no closed form. The bootstrap method is used to estimate the distributions of these point estimators. Different approximations of the interval estimations for the two-parameters are discussed. Real data sets are analyzed to show how this distribution works in practice. A simulation study is performed to investigate the properties of the estimations obtained and compare their performances.

• Journal of the Korea Safety Management & Science
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• 제9권5호
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• pp.43-48
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• 2007

This paper is to present linkage parameter to integrate statistical models and physical models for accelerated life test. Statistical models represent the relationship of probability distribution and life. Physical models show the relationship of life and stress. Moreover, this study proposes the four steps for construction of integrated models for accelerated life test using linkage parameter. Finally, this paper develops new integrated models such as extreme value distribution-general Eyring, linearly increasing failure rate function-general Eyring, etc., and estimates various reliability measures.

• Communications for Statistical Applications and Methods
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• 제28권5호
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• pp.511-520
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• 2021

Over the last decade, Bitcoin has attracted a great deal of public interest and Bitcoin market has grown rapidly. One of the main characteristics of the market is that it often undergoes some events or incidents that cause outlying observations. To obtain reliable results in the statistical analysis of Bitcoin data, these outlying observations need to be carefully treated. In this study, we are interested in change point analysis for Bitcoin return series having such outlying observations. Since these outlying observations can affect change point analysis undesirably, we use a robust test for parameter change to locate change points. We report some significant change points that are not detected by the existing tests and demonstrate that the model allowing for parameter changes is better fitted to the data. Finally, we show that the model with parameter change can improve the forecasting performance of Value-at-Risk.

• Journal of the Korean Statistical Society
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• 제34권3호
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• pp.197-208
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• 2005

We consider the problem for approximate solution of linear stochastic evolution equations driven by infinite-dimensional fractional Brownian motion with Hurst parameter $H\;\in$ (0,1/2). The error of the approximate solution for the explicit Euler scheme is investigated.

• Journal of the Korean Statistical Society
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• 제8권2호
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• pp.99-105
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• 1979

In Thoman and Bain and Schafer and Sheffield, procedures for testing the equality of the scale parameters of two Weibull populations with a common shape parameter and procedures for selecting the Weibull population with the largest scale parameter are given. We give, in this paper, a modified procedure for the above testing and selection problems, which is more powerful than those previoulsy given.