• Communications for Statistical Applications and Methods
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• 제25권3호
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• pp.283-296
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• 2018

Ranked set sampling, as introduced by McIntyre (Australian Journal of Agriculture Research, 3, 385-390, 1952), dealt with the estimation of the mean of one population. To deal with two or more variables, different forms of bivariate and multivariate ranked set sampling were suggested. For a technique to be useful, it should be easy to implement in practice. Bivariate ranked set sampling, as introduced by Al-Saleh and Zheng (Australian & New Zealand Journal of Statistics, 44, 221-232, 2002), is not easy to implement in practice, because it requires the judgment ranking of each of the combination of the order statistics of the two characteristics. This paper investigates two modifications that make the method easier to use. The first modification is based on ranking one variable and noting the rank of the other variable for one cycle, and do the reverse for another cycle. The second approach is based on ranking of one variable and giving the second variable the same rank (Concomitant Order Statistic) for one cycle and do the reverse for the other cycle. The two procedures are investigated for an estimation of the means of some well-known distributions. It is show that the suggested approaches can be used in practice and can be more efficient than using SRS. A real data set is used to illustrate the procedure.

• Journal of the Korean Statistical Society
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• 제25권1호
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• pp.133-144
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• 1996

We, in this paper, propose a nonparametric estimator of bivariate mean residual life function based on Lin and Ying's (1993) bivariate survival function estimator of paired failure times under univariate censoring and prove the uniform consistency and the weak convergence result of this estimator. Through Monte Carlo simulation, the performances of the proposed estimator are tabulated and are illustrated with the skin grafts data.

• Communications for Statistical Applications and Methods
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• 제24권3호
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• pp.271-290
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• 2017

We study a bivariate response regression model with arbitrary marginal distributions and joint distributions using Frank and Clayton's families of copulas. The proposed model is used for fitting dependent bivariate data with explanatory variables using the log-odd log-logistic Weibull distribution. We consider likelihood inferential procedures based on constrained parameters. For different parameter settings and sample sizes, various simulation studies are performed and compared to the performance of the bivariate odd-log-logistic-Weibull regression model. Sensitivity analysis methods (such as local and total influence) are investigated under three perturbation schemes. The methodology is illustrated in a study to assess changes on schoolchildren's oral health-related quality of life (OHRQoL) in a follow-up exam after three years and to evaluate the impact of caries incidence on the OHRQoL of adolescents.

• Journal of the Korean Data and Information Science Society
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• 제22권5호
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• pp.1007-1016
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• 2011

This article deals with the problem of testing for the correlation coefficient in the bivariate normal distribution. We propose Bayesian hypothesis testing procedures for the bivariate normal correlation coefficient under the noninformative prior. The noninformative priors are usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. A simulation study and an example are provided.

• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.655-662
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• 2004

In this paper, we assume that strengths of two components system follow a type II bivariate Pareto model with bivariate type I censored data. And these two components are subjected to a common stress which is independent of the strengths of the components. We obtain estimators for the system reliability based on likelihood function and relative frequency, respectively. Also we construct approximated confidence intervals for the reliability based on maximum likelihood estimator and relative frequency estimator, respectively. Finally we present a numerical study.

• 응용통계연구
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• 제30권2호
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• pp.203-213
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• 2017

우리는 이변량 경시적 자료의 조건부 결합 분포를 추정하기 위하여 회귀 모형과 코플라 모형을 연구하였다. 주변 분포의 추정을 위하여 시변 변환 모형을 고려하였고, 이변량 반응변수 각각에 대한 주변 분포를 가우시안 코플라를 이용하여 결합하여 조건부 결합 분포를 추정하였다. 우리가 제안한 모형은 조건부 평균 모형만으로 자료를 설명하기 어려운 경우에 적용될 수 있다. 시변 변환 모형과 가우시안 코플라 모형을 결합한 본 논문의 방법은 반복 측정된 이변량 경시적 자료에 대한 모형화가 용이하며 해석하기 쉬운 장점이 있다. 우리는 본 논문의 방법을 반복 측정된 이변량 콜레스테롤 자료를 분석하는데 적용하여 보았다.

• Journal of the Korean Statistical Society
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• 제34권2호
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• pp.125-140
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• 2005

In this paper, we consider the estimation of the correlation coefficient in the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) that was introduced by Al-Saleh and Al-Hadhrami (2003a). The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered under different settings. The obtained estimators are compared to their counterparts that are obtained based simple random sampling (SRS). It appears that the suggested estimators are more efficient

• Communications for Statistical Applications and Methods
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• 제10권3호
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• pp.895-907
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• 2003

Recent demands for representing the location of multivariate data produce various multivariate medians such as Tukey median, Oja median and spatial median. They are considered as multivariate versions of the median which is widely recognized as a robust alternative to the arithmetic mean. Many studies show that those multivariate median preserve the robustness. However, the effectiveness of those medians is not fully identified. In this note the relative efficiencies of the multivariate medians are investigated in various configurations under the bivariate t-distribution. It is shown that Tukey median outperforms the others in most configurations.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2015년도 학술발표회
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• pp.239-239
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• 2015

This study presents a bivariate extension of the goodness-of-fit measure for regional frequency distributions developed by Hosking and Wallis [1993] for use with the method of L-moments. Utilising the approximate joint normal distribution of the regional L-skewness and L-kurtosis, a graphical representation of the confidence region on the L-moment diagram can be constructed as an ellipsoid. Candidate distributions can then be accepted where the corresponding the oretical relationship between the L-skewness and L-kurtosis intersects the confidence region, and the chosen distribution would be the one that minimises the Mahalanobis distance measure. Based on a set of Monte Carlo simulations it is demonstrated that the new bivariate measure generally selects the true population distribution more frequently than the original method. An R-code implementation of the method is available for download free-of-charge from the GitHub code depository and will be demonstrated on a case study of annual maximum series of peak flow data from a homogeneous region in Italy.

• Journal of the Korean Data and Information Science Society
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• 제28권1호
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• pp.87-98
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• 2017

일변량 이상의 다변량 경험분포함수의 정의를 새롭게 제안하고, 경험분포함수의 기대값과 분산을 유도하면서 다변량 경험분포함수가 실제의 분포함수로 수렴함을 확인한다. 그리고 다양한 상관계수의 이변량 표준정규분포에서 추출한 확률표본을 바탕으로 이변량 경험분포함수를 구하고 이를 이차원 평면에 시각적으로 표현하는 두 종류의 그래픽적인 방법을 제안한다. 하나는 계단으로 표현하여 계단식 함수와 유사한 성격을 갖고 있는 방법이고, 다른 하나는 이변량 분위벡터로 설명되는 그림 방법이다. 두 종류의 시각적인 표현 방법은 삼차원으로 표현할 수 있으나 이차원 평면으로도 쉽게 구현이 가능하며, 일반적으로 이변량 누적분포함수의 모든 특징을 충분히 설명할 수 있다. 따라서 삼변량 경험분포함수를 시각적 표현이 가능함을 보인다. 이변량과 사변량의 실증 예제를 통하여 본 연구에서 제안한 다변량 경험분포함수와 이차원 평면에 표현하는 시각적인 표현 방법들을 구현하고 탐색한다.