• Communications for Statistical Applications and Methods
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• 제15권4호
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• pp.483-496
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• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Journal of the Korean Data and Information Science Society
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• 제15권1호
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• pp.31-39
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• 2004

In this paper, we consider two components system which the lifetimes follow bivariate pareto model with bivariate random censored data. We assume that the censoring times are independent of the lifetimes of the two components. We develop large sample test for testing independence between two components. Also we present a simulation study which is the test based on asymptotic normal distribution in testing independence.

• 대한수학회논문집
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• 제34권1호
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• pp.239-251
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• 2019

In this paper we introduce a new formulation of symmetric homogeneous bivariate means that depends on the variation of a given continuous strictly increasing function on (0, ${\infty}$). It turns out that this class of means includes a lot of known bivariate means among them the arithmetic mean, the harmonic mean, the geometric mean, the logarithmic mean as well as the first and second Seiffert means. Using this new formulation we introduce a lot of new bivariate means and derive some mean-inequalities.

• Communications for Statistical Applications and Methods
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• 제19권4호
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• pp.629-638
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• 2012

We propose some methods to obtain optimal thresholds and classification functions by using various cutoff criterion based on the bivariate ROC curve that represents bivariate cumulative distribution functions. The false positive rate and false negative rate are calculated with these classification functions for bivariate normal distributions.

• 응용통계연구
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• 제22권2호
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• pp.341-353
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• 2009

두 군의 처리를 비교하는 임상시험에서 효능(efficacy)과 안전성(safety)이 동일하게 중요한 변수로 취급되는 경우에 이변량(bivariate) 반응변수로서 분석되고 연구계획의 단계에서도 이변량 표본수 결정방법이 사용되어야 한다. Thall과 Cheng (1999)은 효능과 안전성의 반응값이 이변량 이항(bivariate binary) 변수인 경우의 표본수 결정방법을 제시하였으며, 본 연구에서는 목표모수 설정과정은 기존의 연구와 같으나 월콕슨-만-휘트니(Wilcoxon-Mann-Whitney: WMW) 통계량에 근거한 검정법과 표본수 결정방법을 제시한다. Thall과 Cheng (1999)의 검정통계량은 변수 변환시킨 비율의 근사 정규성에 근거하는 반면에, WMW 통계량은 확률에 근거한 비모수적 방법으로 이변량 이항변수 뿐만 아니라 이변량 순위변수로 측정된 반응값에도 적용시킬 수 있다 Thall과 Cheng (1999)에 제시한 항암치료 임상연구의 두 예제에 위의 두 다른 방법으로 계산된 표본수를 비교한 결과, Thall과 Cheng (1999)의 첫째 예제에서는 이변량 WMW 방법에 의한 표본수가 더욱 작았으나 둘째 예제에서는 더욱 큰 것으로 나타났다.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2003년도 추계학술대회
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• pp.31-38
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• 2003

In this paper, we obtain the estimator of system reliability for the bivariate Pareto model with bivariate type 1 censored data. We obtain the estimators and approximated confidence intervals of the reliability for the parallel system based on likelihood function and the relative frequency, respectively. Also we present a numerical example by giving a data set which is generated by computer.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.37-46
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• 2020

Recurrent event data frequently occur in clinical studies, demography, engineering reliability and so on (Cook and Lawless, The Statistical Analysis of Recurrent Events, Springer, 2007). Sometimes, two or more different but related type of recurrent events may occur simultaneously. In this study, our interest is to estimate the covariate effect on bivariate recurrent event times with zero inflations. Such zero inflation can be related with susceptibility. In the context of bivariate recurrent event data, furthermore, such susceptibilities may be different according to the type of event. We propose a joint model including both two intensity functions and two cure rate functions. Bivariate frailty effects are adopted to model the correlation between recurrent events. Parameter estimates are obtained by maximizing the likelihood derived under a piecewise constant hazard assumption. According to simulation results, the proposed method brings unbiased estimates while the model ignoring cure rate models gives underestimated covariate effects and overestimated variance estimates. We apply the proposed method to a set of bivariate recurrent infection data in a study of child patients with leukemia.

• 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.

• 대한수학회논문집
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• 제24권4호
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• pp.553-559
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• 2009

In the paper, some new inequalities for certain bivariate means are obtained, which extend some known results.

• Journal of the Korean Data and Information Science Society
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• 제28권5호
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• pp.959-970
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• 2017

본 연구에서는 두 변수의 상관계수를 반영한 이변량 자료의 왜도와 첨도 통계량을 제안하고, 시각적으로 표현할 수 있는 표면그림을 개발한다. 이변량 왜도 통계량은 이변량 확률표본 자료의 치우침 방향과 정도를 표현하는 실수 한 쌍으로 정의한다. 첨도는 양의 값을 가지며 이변량 정규분포를 기준으로 꼬리 부분의 두터운 정도를 파악할 수 있다. 그리고 표면그림은 분위벡터를 바탕으로 평면에 구현한다. 다양한 형태의 이변량 자료를 생성하여 표면그림을 작성하고 왜도와 첨도를 계산하여 탐색해 본 결과, 왜도와 첨도 값들은 표면그림으로 구현한 이변량 자료의 특징을 잘 반영하는 것을 발견할였다. 그러므로 본 논문에서 제안한 왜도, 첨도 그리고 표면그림은 이변량 분포를 분석하는 기술통계학적 방법으로 활용할 수 있다.