• Journal of the Korean Data and Information Science Society
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• 제14권4호
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• pp.1091-1102
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• 2003

The Weibull variate is commonly used as a lifetime distribution in reliability applications. Estimation of parameters is revisited in the two-parameter Weibull distribution. The method of product spacings, the method of quantile estimates and the method of least squares are applied to this distribution. A comparative study between a simple minded estimate, the maximum likelihood estimate, the product spacings estimate, the quantile estimate, the least squares estimate, and the adjusted least squares estimate is presented.

• 응용통계연구
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• 제26권6호
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• pp.915-922
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• 2013

분위수 회귀는 반응변수의 조건부 분위수 함수를 추정함으로써 반응변수와 예측변수의 관계에 대한 포괄적인 정보를 제공한다. 그러나 여러 개의 분위수 함수를 개별적으로 추정하게 되면 이들이 서로 교차할 가능성이 있으며, 이러한 분위수 함수의 교차(quantile crossing) 현상 분위수의 이론적 기본 특성에 위배된다. 본 논문에서는 다중 비교차 분위수 함수의 추정을 위해 커널 계수에 제약식을 부여하는 순차적 추정법을 제안하였으며, 모의실험을 통해 제안한 방법론의 효율적인 성능과 유용성을 확인하였다.

• 한국수자원학회:학술대회논문집
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• 한국수자원학회 2004년도 학술발표회
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• pp.256-261
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• 2004

Due to the problems of global warming, the frequency of meteorological extremes such as droughts, floods and the annual rainfall amount are suddenly increasing. Even though the increase of greenhouse gases, for example, is thought to be the main factor for global warming, its impact on global climate has not yet been revealed clearly in rather quantitative manners. Therefore, tile objective of this study is to inquire the change of precipitation condition due to climate change by global warming. In brief, this study want to see its assumption if rainfall quantile estimates are really changing. In order to analyze the temporal change, the rainfall quantile estimates at the Seoul rain gauge stations are estimated for the 21-year data period being moved from 1908 to 2002 with 1-year lag. The main objective of this study is to analyze the variability of rainfall quantile estimates using four methods. Next, The changes in confidence interval of rainfall quantile are evaluated by increasing the data period. It has been found that confidence interval of rainfall quantile estimates is reduced as the data period increases. When the hydraulic structures are to be designed, it is important to select the data size and to re-estimate the flood prevention capacity in existing river systems.

• Journal of the Korean Data and Information Science Society
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• 제8권1호
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• pp.49-58
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• 1997

We consider the quantile function for the bootstrapped product limit estimate under left truncation and right censoring model and show its weak convergence. We also obtain bootstrapped confidence bands for the quantile function.

• 지구물리
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• 제5권2호
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• pp.131-142
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• 2002

일반적으로 지자기 전달함수는 관측치와 예측치의 차이를 최소화하는 관점에서 해가 추정된다. 오차의 구조가 가우스 분포를 따르면 최소자승 추정이 최적의 추정이지만, 그렇지 않은 경우 전달 함수 추정을 심각하게 왜곡시킬 수 있으므로 오차 구조에 대한 정보가 요구된다. 본 연구에서는 Q-Q plot을 이용한 오차 구조으 검증을 통하여 실제 오차 구조에 대한 정보를 획득하였고 가우스 분포 가정을 벗어나는 오차 구조에 대해 외치(outlier)에 의한 영향을 최소로 하며 해를 추정하는 로버스트 추정(regression M-estimate)을 적용하였다. 오차가 가우스 분포를 따르는 경우, 최소자승 추정과 로버스트 추정은 유사한 결과를 나타내나, 오차가 가우스 분포를 벗어나는 경우 로버스트 추정이 최소자승 추정보다 부드러운 결과를 나타냄을 확인하였다.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.807-818
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• 2005

In this paper we propose an estimation method for regression quantiles with left-truncated and right-censored data. The estimation procedure is based on the weight determined by the Kaplan-Meier estimate of the distribution of the response. We show how the proposed regression quantile estimators perform through analyses of Stanford heart transplant data and AIDS incubation data. We also investigate the effect of censoring on regression quantiles through simulation study.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.473-481
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• 2001

Shapiro and Wilk (1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test statistic is inconsistent. Kim(2001) proposed a modified Shapiro-Wilk's test statistic based on the ratio of tow asymptotically efficient estimates of scale. In this paper, we study the asymptotic behavior of the statistic using the approximation of the quantile process by a sequence of Brownian bridges and represent the limit null distribution as an integral of a Brownian bridge.

• 응용통계연구
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• 제29권5호
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• pp.773-786
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• 2016

분위수 회귀는 반응변수의 조건부 분위수 함수를 추정함으로써 반응변수와 예측변수의 관계에 대한 포괄적인 정보를 제공한다. 그러나 여러 개의 분위수 함수를 개별적으로 추정하게 되면 이들이 서로 교차할 가능성이 있으며, 이러한 분위수 함수의 교차(quantile crossing) 현상 분위수의 이론적 기본 특성에 위배된다. 본 논문에서는 다중 비교차 분위수 함수의 추정의 대표적인 방법들의 특성을 적합식과 계산 알고리즘의 측면에서 살펴보고, 모의실험과 실제 자료 분석을 통해 그 성능을 비교하였다.

• Structural Engineering and Mechanics
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• 제32권1호
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• pp.127-145
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• 2009

A novel approach is proposed to effectively estimate the quantile functions of normalized performance indices of reliability constraints in a reliability-based optimization (RBO) problem. These quantile functions are not only estimated as functions of exceedance probabilities but also as functions of the design variables of the target RBO problem. Once these quantile functions are obtained, all reliability constraints in the target RBO problem can be transformed into non-probabilistic ordinary ones, and the RBO problem can be solved as if it is an ordinary optimization problem. Two numerical examples are investigated to verify the proposed novel approach. The results show that the approach may be capable of finding approximate solutions that are close to the actual solution of the target RBO problem.

• Communications for Statistical Applications and Methods
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• 제21권4호
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• pp.285-296
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• 2014

The quantile residual life function has been effectively used to interpret results from the analysis of the proportional hazards model for censored survival data; however, the quantile residual life function is not always estimable with currently available semi-parametric regression methods in the presence of heavy censoring. A parametric regression approach may circumvent the difficulty of heavy censoring, but parametric assumptions on a baseline hazard function can cause a potential bias. This article proposes a Bayesian semi-parametric regression approach for inference on an unknown baseline hazard function while adjusting for available covariates. We consider a model-based approach but the proposed method does not suffer from strong parametric assumptions, enjoying a closed-form specification of the parametric regression approach without sacrificing the flexibility of the semi-parametric regression approach. The proposed method is applied to simulated data and heavily censored survival data to estimate various quantile residual lifetimes and adjust for important prognostic factors.