• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.933-939
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• 2009

The bivariate data in clinical research fields often has two types of failure times, which are mark variable for the first failure time and the final failure time. This paper showed how to generate bootstrap data to get Bayesian estimation for the joint distribution of bivariate survival times. The observed data was generated by Frank's family and the fake date is simulated with the Gamma prior of survival time. The bootstrap data was obtained by combining the mimic data with the observed data and the simulated fake data from the observed data.

• Communications for Statistical Applications and Methods
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• 제25권5호
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• pp.523-544
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• 2018

Bivariate distributions play a fundamental role in survival and reliability studies. We consider a regression model for bivariate survival times under right-censored based on the bivariate Kumaraswamy Weibull (Cordeiro et al., Journal of the Franklin Institute, 347, 1399-1429, 2010) distribution to model the dependence of bivariate survival data. We describe some structural properties of the marginal distributions. The method of maximum likelihood and a Bayesian procedure are adopted to estimate the model parameters. We use diagnostic measures based on the local influence and Bayesian case influence diagnostics to detect influential observations in the new model. We also show that the estimates in the bivariate Kumaraswamy Weibull regression model are robust to deal with the presence of outliers in the data. In addition, we use some measures of goodness-of-fit to evaluate the bivariate Kumaraswamy Weibull regression model. The methodology is illustrated by means of a real lifetime data set for kidney patients.

• Composites Research
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• 제29권5호
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• pp.299-305
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• 2016

본 연구는 이변량 Gaussian 분포함수를 적용하여 CFRP 적층판의 섬유물성 변화를 추정하는 방법을 제안하였다. 섬유의 손상 분포를 규명하기 위하여 수정된 이변량 Gaussian 분포함수를 적용하여 5개의 미지 변수가 고려되었다. 조합된 컴퓨터 기법을 적용하여 역문제를 해결하기 위하여 본 연구에서는 몇 개의 고유진동수와 모드 정보를 입력데이터로 활용하였다. 수치해석 예제는 제안된 기법이 적층배열 변화에 따른 CFRP 판의 섬유 손상 분포 및 위치를 규명할 수 있는 적합하고 실용적은 방법임을 보여준다.

• Smart Structures and Systems
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• 제21권5호
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• pp.601-609
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• 2018

The estimated probabilistic model of wind data based on the conventional approach may have high discrepancy compared with the true distribution because of the uncertainty caused by the instrument error and limited monitoring data. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method has been developed in the companion paper and is conducted to formulate the joint probability density function (PDF) of wind speed and direction using the wind monitoring data of the investigated bridge. The established bivariate model of wind speed and direction only represents the features of available wind monitoring data. To characterize the stochastic properties of the wind parameters with the subsequent wind monitoring data, in this study, Bayesian inference approach considering the uncertainty is proposed to update the wind parameters in the bivariate probabilistic model. The slice sampling algorithm of Markov chain Monte Carlo (MCMC) method is applied to establish the multi-dimensional and complex posterior distribution which is analytically intractable. The numerical simulation examples for univariate and bivariate models are carried out to verify the effectiveness of the proposed method. In addition, the proposed Bayesian inference approach is used to update and optimize the parameters in the bivariate model using the wind monitoring data from the investigated bridge. The results indicate that the proposed Bayesian inference approach is feasible and can be employed to predict the bivariate distribution of wind speed and direction with limited monitoring data.

• Communications for Statistical Applications and Methods
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• 제15권2호
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• pp.193-204
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• 2008

In this paper we study some positive dependence concepts, introduced by Caperaa and Genest (1990) and Shaked (1977b), for bivariate lomax distribution. In particular, we obtain some measures of association for this distribution and derive the tail-dependence coefficients by using copula function. We also compare Spearman's $\rho_s$ with Kendall's $\tau$ for bivariate lomax distribution.

• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.237-244
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• 2014

It is known that the dierence in the length between two location parameters of two random variables is equivalent to the difference in the area between two cumulative distribution functions. In this paper, we suggest two applications by using the difference of distribution functions. The first is that the difference of expectations of a certain function of two continuous random variables such as the differences of two kth moments and two moment generating functions could be defined by using the difference between two univariate distribution functions. The other is that the difference in the volume between two empirical bivariate distribution functions is derived. If their covariance is estimated to be zero, the difference in the volume between two empirical bivariate distribution functions could be defined as the difference in two certain areas.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.187-196
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• 2002

Testing for normality has always been a center of practical and theoretical interest in statistical research. In this paper a test statistic for bivariate normality is proposed. The underlying idea is to investigate all the possible linear combinations that reduce to the standard normal distribution under the null hypothesis and compare the order statistics of them with the theoretical normal quantiles. The suggested statistic is invariant with respect to nonsingular matrix multiplication and vector addition. We show that the limit distribution of an approximation to the suggested statistic is represented as the supremum over an index set of the integral of a suitable Gaussian Process. We also simulate the null distribution of the statistic and give some critical values of the distribution and power results.

• Communications for Statistical Applications and Methods
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• 제19권2호
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• pp.277-286
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• 2012

신용평가모형에서 부도로 잘못 예측된 정상 차주의 비율과 정확하게 평가된 부도차주의 비율인 일변량 누적분포함수로 표현된 ROC 곡선을 이용하여 분류성과를 평가한다. 본 연구에서는 스코어 확률변수를 이변량으로 확장하여 부도와 정상 차주의 결합누적분포함수를 이용하여 표현할 수 있는 ROC 곡선을 제안한다. 이변량 평균벡터를 통과하는 확률변수의 선형 관계를 이용하여 이변량 ROC 곡선을 구현한다. 그리고 다양한 이변량 정규분포에 대한 ROC 곡선으로부터 분류성과를 탐색하고, 이에 대응하는 AUROC 통계량과 비교분석한다. 본 연구에서 제안한 이변량 ROC 곡선으로부터 분류기준에 적합한 최적분류점을 구하고 이를 통해 이변량 혼합분포함수의 최적 분류기준을 설정할 수 있음을 보인다.

• 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.

• 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.