• Communications for Statistical Applications and Methods
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• 제22권6호
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• pp.599-604
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• 2015

Kendall's tau statistic has been applied to test an association of bivariate random variables. However, incomplete bivariate data with a truncation and a censoring results in incomparable or unorderable pairs. With such a partial information, Tsai (1990) suggested a conditional tau statistic and a test procedure for a quasi independence that was extended to more diverse cases such as double truncation and a semi-competing risk data. In this paper, we also employed a conditional tau statistic to estimate an association of bivariate interval censored data. The suggested method shows a better result in simulation studies than Betensky and Finkelstein's multiple imputation method except a case in cases with strong associations. The association of incubation time and infection time from an AIDS cohort study is estimated as a real data example.

• Journal of the Korean Data and Information Science Society
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• 제18권2호
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• pp.553-560
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• 2007

In this paper, we consider two components system which lifetimes have Freund's bivariate exponential model with equal failure rates. We propose Bayesian multiple comparisons procedure for the failure rates of I Freund's bivariate exponential populations based on Dirichlet process priors(DPP). The family of DPP is applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through Markov Chain Monte Carlo(MCMC) method, namely, Gibbs sampling, due to the intractability of analytic evaluation. The whole process of multiple comparisons problem for the failure rates of bivariate exponential populations is illustrated through a numerical example.

• 응용통계연구
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• 제25권1호
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• pp.115-123
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• 2012

In animal tumorigenicity data, tumor onsets occur at several sites and onset times cannot be exactly observed. Instead, the existence of tumors is examined only at death time or sacrifice time of the animal. Such an incomplete data structure makes it difficult to investigate the effect of treatment on tumor onset times; in addition, such dependence should be considered when censoring due to death is related with tumor onset. A bivariate frailty effect is incorporated to model bivariate tumor onsets and to connect death with tumor. For the inference of parameters, EM algorithm is applied and a real NTP(National Toxicology Program) dataset is analyzed as an illustrative example.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.37-45
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• 1999

본 논문에서는 Marshall-Olkin의 이변량 지수모형을 따르는 두 부품의 수명들이 이변량 임의 중단된 자료로 관찰되는 경우를 생각한다. 이 경우 모수와 시스템 신뢰도에 대한 최우추정량을 구하고 근사적 정규성을 이용하여 두 부품의 수명에 대한 동일성 및 독립성 검정법을 제안한다. 그리고 모의실험을 통하여 제안된 추정량들과 검정법들의 유의확률을 계산한다.

• Journal of the Korean Data and Information Science Society
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• 제26권6호
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• pp.1495-1500
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• 2015

We obtain means and variances of max {X, Y} and min {X, Y} in the underlying Morgenstern type bivariate uniform variables X and Y with same scale parameters and different scale parameters respectively. And we obtain the conditional expectations in the underlying Morgenstern type bivariate uniform variables. Here, we shall consider the conditional expectations to know the dependence of one variable on the other variable and we consider the behaviors of means and variances of max {X, Y} and min {X, Y} with respect to changes in means, variances, and the correlation coeffcient of the underlying Morgenstern type bivariate uniform variables.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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• pp.1391-1396
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• 2008

In this paper, we consider two components system which the lifetimes have Marshall and Olkin's bivariate exponential model with bivariate type I censored data. We propose a Bayesian independent test procedure for above model using fractional Bayes factor method by O'Hagan based on improper prior distributions. And we compute the fractional Bayes factor and the posterior probabilities for the hypotheses, respectively. Also we select a hypothesis which has the largest posterior probability. Finally a numerical example is given to illustrate our Bayesian testing procedure.

• 품질경영학회지
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• 제42권1호
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• pp.1-14
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• 2014

Purpose: In this paper, the minimal repair-replacement warranty policy is used to carry out a warranty cost analysis with warranty servicing times and failure times that are statistically correlated to bivariate distributions. Methods: Based on the developed approach by Park and Pham (2012a), we investigate the property of the Freund's bivariate exponential distribution and obtain the number of warranty services using the field data to conduct the warranty cost analysis. Results: Maximum likelihood estimates are presented to estimate the parameters and the warranty model is investigated using a Freund's bivariate exponential distribution. A numerical example is discussed to deal with the applicability of the developed approach in the paper. Conclusion: A novel approach of analyzing the warranty cost is proposed for a product in which failure times and warranty servicing times are used simultaneously to investigate the eligibility of a warranty claim.

• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.385-397
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• 2016

The stress-strength models have been intensively investigated in the literature in regards of estimating the reliability ${\theta}$ = P(X > Y) using parametric and nonparametric approaches under different sampling schemes when X and Y are independent random variables. In this paper, we consider the problem of estimating ${\theta}$ when (X, Y) are dependent random variables with a bivariate underlying distribution. The empirical and kernel estimates of ${\theta}$ = P(X > Y), based on bivariate ranked set sampling (BVRSS) are considered, when (X, Y) are paired dependent continuous random variables. The estimators obtained are compared to their counterpart, bivariate simple random sampling (BVSRS), via the bias and mean square error (MSE). We demonstrate that the suggested estimators based on BVRSS are more efficient than those based on BVSRS. A simulation study is conducted to gain insight into the performance of the proposed estimators. A real data example is provided to illustrate the process.

• 물과 미래
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• 제28권2호
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• pp.145-154
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• 1995

강우량 자료들을 수공계획에 적절히 사용하기 위해서는 강우량에 대한 다양한 해석기법이 필요하다. 본 연구에서는 연속강우량에 따른 강우사상계열의 수문빈도해석을 위한 확률분포를 연구한 것이다. 2변량 정규분포, 2변량 대수정규분포, 2변량 gamma 분포가 강릉, 서울, 인천, 추풍령, 대구, 전주, 광주, 부산지점의 연속최대 강우량과 그 지속기간으로 이루어진 강우사상의 확률분포로서 적용되었다. 이들 지점의 강우사상 자료가 2변량 정규분포, 2변량 대수정규분포에는 적합되었으나 2변량 gamma 분포에는 적합되지 않았다. 적합도 검정을 통하여 선정된 최적 분포형으로부터 확률강우사상의 빈도곡선을 제시하였다.

• 응용통계연구
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• 제23권3호
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• pp.585-594
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• 2010

본 연구에서는 제로절단된 이변량 일반화 포아송 분포에서 두 반응변수간 산포모수의 효과에 대하여 연구하였다. 모의실험 결과 두 반응변수가 서로 다른 산포를 갖는 경우 이를 무시하는 이변량 포아송 분포나 이변량 음이항 분포에 의한 모형적합은 효율성이 떨어지는 것으로 나타났다. 아울러 본 연구에서는 이와 같은 상이한 산포의 존재유무에 대한 가설검정에서 스코어 검정을 유도하고 우도비 검정과 효율성을 비교하였다.