• 대한수학회보
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• 제36권3호
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• pp.451-457
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• 1999

This paper provides sufficient conditions which ensure the strong consistency of regression quantiles estimators of nonlinear regression models. The main result is supported by the application of an asymptotic property of the least absolute deviation estimators as a special case of the proposed estimators. some example is given to illustrate the application of the main result.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.289-302
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• 2004

The asymptotic dependence between the central quasi-ranges and empirical quantiles was studied. The asymptotic dependence are obtained when the sample size is a positive integer valued random variable (r. v.). The dependence conditions and limit forms are obtained under generl conditions such as : the interrelation of the basic variables (the original random sample) and the random sample size is not restricted. In additition the normalizing constants do not depend on the random size.

• Journal of the Korean Data and Information Science Society
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• 제10권1호
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• pp.1-10
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• 1999

Table of the empirical quantiles for the well known Shapiro-Francia W' goodness of fit statistic is produced which is more accurate than the existing ones. Prediction equation for the quantiles of W' statistic for sample sizes 30 or more we developed. The process of computing the expected values for the standard normal variate is discussed. This work is intended to make the Shapiro-Francia W' statistic more accessible to the practitioner.

• Communications for Statistical Applications and Methods
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• 제11권3호
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• pp.447-454
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• 2004

In this paper, we consider the bootstrap method to the interval estimation of the difference of quantiles of right censored data. We showed the validity of bootstrap method and compare with others with real data example. In simulation various resampling schemes for right censored data are also considered.

• Journal of the Korean Statistical Society
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• 제30권4호
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• pp.667-678
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• 2001

The asymptotic behavior and distribution for quantiles estimators using ranked samples are introduced. Applications of quantiles estimation on finding the normal ranges (2.5% and 97.5% percentiles) and the median of some medical characteristics and on finding the Hodges-Lehmann estimate are discussed. The conclusion of this study is, whenever perfect ranking is possible, the relative efficiency of quantiles estimation using ranked samples relative to SRS is high. This may translates to large savings in cost and time. Also, this conclusion holds even if the ranking is not perfect. Computer simulation results are given and real data from lows 65+ study is used to illustrate the method.

• Communications for Statistical Applications and Methods
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• 제23권2호
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• pp.119-129
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• 2016

A new sampling method is introduced based on the idea of a ranked set sampling scheme in which taken samples in each set are dependent on previous ones. Some theoretical results are presented and distribution-free confidence intervals are derived for the quantiles of any continuous population. It is shown numerically that the proposed sampling scheme may lead to 95% confidence intervals (especially for extreme quantiles) that cannot be found based on the ordinary ranked set sampling scheme presented by Chen (2000) and Balakrishnan and Li (2006). Optimality aspects of this scheme are investigated for both coverage probability and minimum expected length criteria. A real data set is also used to illustrate the proposed procedure. Conclusions are eventually stated.

• Journal of the Korean Data and Information Science Society
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• 제18권3호
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• pp.833-845
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• 2007

When X and Y have independent exponential distributions, we develop a Bayesian testing procedure for the ratio of two quantiles under reference prior. The noninformative prior such as reference prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we develop a Bayesian testing procedure based on fractional Bayes factor and intrinsic Bayes factor. We show that the posterior density under the reference prior is proper and propose the Bayesian testing procedure for the ratio of two quantiles using fractional Bayes factor and intrinsic Bayes factor. Simulation study and a real data example are provided.

• 대한수학회보
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• 제51권5호
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• pp.1399-1409
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• 2014

In this article, we establish the $\mathfrak{F}_p$-uniform moderate deviation principles of the sample quantiles and order statistics for a sequence of independent and identically distributed samples.

• Communications for Statistical Applications and Methods
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• 제7권3호
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• pp.913-926
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• 2000

An electronic statistics text on the web is implemented. The introduced text provide interactive instructions on the statistical estimation and inference. As a by-product, we also provide a calculation of quantiles and p-value of t-distribution and standard normal distribution. This program was written in JAVA programming language.

• 한국수자원학회논문집
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• 제41권4호
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• pp.405-412
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• 2008

본 연구에서는 지역빈도해석 기법 중 하나인 FORGEX 기법을 이용하여 확률강우량을 추정하였다. 기존의 원형 네트워크와 1:1.5, 1:2의 비율을 갖는 타원형 네트워크가 한국의 강우자료에 적합한 방법인지를 판단하기 위해 3 가지 경우를 비교 분석하였다. 이 분석을 위해서 남한지역의 376개 지점의 연최대강우자료를 추출하고, 이 자료들을 연최대자료의 중간값으로 표준화하였다. 네트워크는 분석 대상 지점을 중심으로 형성되며, pooled points와 netmax 자료를 각 네트워크에서 매년 추출한다. 그리고 성장곡선(growth curve)을 유도하고 주어진 재현기간에 따른 확률강우량을 추정한다. 지점빈도해석과 지역빈도해석의 대표적인 기법인 홍수지수법(index flood method), FORGEX 기법이 적용되었고, 이를 통해 얻은 결과를 비교 분석하였다. 또한 36개 지점에 원형과 타원형 네트워크를 이용한 FORGEX 기법을 적용하였고, 그 결과를 비교 분석하였다. 결과적으로 대상지점의 지점빈도해석으로 구한 확률강우량과 지역빈도해석으로 구한 확률강우량의 차이가 적을 때 원형과 타원형 네트워크의 추정된 확률강우량의 차이도 적었다. 그러나 지점빈도해석의 결과와 홍수지수법 결과의 차이가 클 때 원형과 타원형 네트워크로 추정된 확률강우량의 차이도 컸다. 타원형 네트워크가 더 많은 지점을 포함할 때, 타원으로부터 추정된 확률강우량 값은 원으로 구해진 값보다 높은 정확도를 보였다. 그리고 타원의 비율이 1:2일 때가 1:1.5보다 홍수지수법으로 구한 확률강우량 값에 가까웠다. 그러므로 1:2 비율의 타원을 적용한 FORGEX 기법이 한국의 지역빈도해석에 적합한 방법이라 할 수 있다.