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

• Communications for Statistical Applications and Methods
• /
• 제30권6호
• /
• pp.531-550
• /
• 2023

The estimation of extreme quantiles is one of the main objectives of statistics of extremes (which deals with the estimation of rare events). In this paper, a robust estimator of extreme quantile of a heavy-tailed distribution is considered. The estimator is obtained through the minimum density power divergence criterion on an exponential regression model. The proposed estimator was compared with two estimators of extreme quantiles in the literature in a simulation study. The results show that the proposed estimator is stable to the choice of the number of top order statistics and show lesser bias and mean square error compared to the existing extreme quantile estimators. Practical application of the proposed estimator is illustrated with data from the pedochemical and insurance industries.

• 응용통계연구
• /
• 제25권1호
• /
• pp.101-114
• /
• 2012

자동차보험의 손해율이란 지급보험금의 수입보험료에 대한 비율을 의미한다. 손해율이 매우 큰 값을 갖는 대형손실이 일어나는 경우에는 보험회사의 재무적인 부분에 큰 악영향을 미치게 된다. 따라서 보험회사가 이에 대비할 수 있도록 하기 위하여 손해율의 극단 분위수(extreme quantile)를 추정하는 것은 매우 중요한 일이다. 다른 종류의 보험 관련 데이터와 같이 손해율의 분포는 오른쪽으로 긴 꼬리를 갖는 두꺼운 꼬리분포(heavy-tailed distribution)를 갖는다. 이런 자료에서 극단 분위수룰 추정하기 위하여 가장 많이 사용되는 방법론은 POT(Peaks over threshold)와 Hill 추정(Hill estimation)이다. 본 논문에서는 일반화파레토분포(generalized Pareto distribution; GPD)의 다양한 모수추정방법론의 성능을 모의실험과 실제 손해율 데이터를 사용하여 비교, 분석하였다. 또한 Hill 추정치를 사용하여 극단 분위수를 추정하였다. 그 결과 대부분의 경우에 POT 방법론이 Hill 추정치를 이용한 방법보다 정확한 분위수를 추정하였고, 모수추정방법론 중에서는 MLE, Zhang, NLS-2 방법론이 가장 좋은 결과를 보여주었다.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2017년도 학술발표회
• /
• pp.228-232
• /
• 2017

Extreme hydrological events can cause serious threats to the society. Hence, the selection of probability distributions for extreme rainfall is a fundamental issue. For this reason, this study was focused on understanding possible distributional changes in annual daily maximum rainfalls (AMRs) over time in Sri Lanka using quantile regression. A simplified nine-category distributional-change scheme based on comparing empirical probability density function of two years (i.e. the first year and the last year), was used to determine the distributional changes in AMRs. Daily rainfall series of 13 station over Sri Lanka were analyzed for the period of 1960-2015. 4 distributional change categories were identified for the AMRs. 5 stations showed an upward trend in all the quantiles (i.e. 9 quantiles: from 0.05 to 0.95 with an increment of 0.01 for the AMR) which could give high probability of extreme rainfall. On the other hand, 8 stations showed a downward trend in all the quantiles which could lead to high probability of the low rainfall. Further, we identified a considerable spatial diversity in distributional changes of AMRs over Sri Lanka.

• Wind and Structures
• /
• 제34권6호
• /
• pp.469-482
• /
• 2022

The generalized extreme value distribution (GEVD) is frequently used to fit the block maximum of environmental parameters such as the annual maximum wind speed. There are several methods for estimating the parameters of the GEV distribution, including the least-squares method (LSM). However, the application of the LSM with the expected order statistics has not been reported. This study fills this gap by proposing a fitting method based on the expected order statistics. The study also proposes a plotting position to approximate the expected order statistics; the proposed plotting position depends on the distribution shape parameter. The use of this approximation for distribution fitting is carried out. Simulation analysis results indicate that the developed fitting procedure based on the expected order statistics or its approximation for GEVD is effective for estimating the distribution parameters and quantiles. The values of the probability plotting correlation coefficient that may be used to test the distributional hypothesis are calculated and presented. The developed fitting method is applied to extreme thunderstorm and non-thunderstorm winds for several major cities in Canada. Also, the implication of using the GEVD and Gumbel distribution to model the extreme wind speed on the structural reliability is presented and elaborated.

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

• 한국수자원학회논문집
• /
• 제45권3호
• /
• pp.263-274
• /
• 2012

최근 다양한 기후변동성으로 인해 전 세계적으로 극한호우사상이 동시다발적으로 일어나고 있다. 우리나라의 극한호우사상은 주로 여름철 태풍으로 인한 호우와 국지성 집중호우에 의해서 발생한다. 극한호우사상에 대한 적절한 확률강우량을 추정하기 위해서, 본 연구에서는 연최대치일강우를 태풍으로 인한 강우와 집중호우로 인한 강우로 구분하여 확률적 거동을 고려하였다. 일반적인 강우빈도해석법은 연최대치강우가 단일 모집단을 이룬다고 가정하여 단일 분포함수를 적용하여 확률강우량을 추정하는 반면, 본 연구에서는 연최대치강우를 구성하는 두 가지 호우의 통계적 특성을 수문빈도해석에서 고려하기 위해, 혼합 분포함수를 적용하였다. 비교적 긴 관측강우자료를 보유한 15개 지점을 선정하여, 일강우량에 대한 확률강우량을 산정하고 비교분석을 실시하였다. 혼합 검벨분포모형에 의한 확률강우량은 단일 검벨분포함수를 적용한 확률강우량과 비교하여 지역에 따라 증감이 나타났으며, 이러한 결과는 홍수방어시스템의 계획 및 설계에서 유용한 정보를 제공할 것이다.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 1997년도 학술발표회 논문집
• /
• pp.340-345
• /
• 1997

• Wind and Structures
• /
• 제15권2호
• /
• pp.87-109
• /
• 2012

A substantial part of South Africa is subject to more than one strong wind source. The effect of that on extreme winds is that higher quantiles are usually estimated with a mixed strong wind climate estimation method, compared to the traditional Gumbel approach based on a single population. The differences in the estimated quantiles between the two methods depend on the values of the Gumbel distribution parameters for the different strong wind mechanisms involved. Cluster analysis of the distribution parameters provides a characterization of the effect of the relative differences in their values, and therefore the dominance of the different strong wind mechanisms. For gusts, cold fronts tend to dominate over the coastal and high-lying areas, while other mechanisms, especially thunderstorms, are dominant over the lower-lying areas in the interior. For the hourly mean wind speeds cold fronts are dominant in the south-west, south and east of the country. On the West Coast the ridging of the Atlantic Ocean high-pressure system dominate in the south, while the presence of a deep trough or coastal low pressure system is the main strong wind mechanism in the north. In the central interior cold fronts tend to share their influence almost equally with other synoptic-scale mechanisms.

• 응용통계연구
• /
• 제20권1호
• /
• pp.1-9
• /
• 2007

한국의 네 개 도시(서울, 대구, 춘천, 영천)의 일일 최고기온을 모형화하여, 이에 적합한 분포를 제안하고 분포의 적합성을 여러 가지 방법에 의하여 검토하였다. 제안된 분포는 극단간 분포의 일종이며, 적합성 검토는 카이제곱 적합도 검정, Q-Q plot,확률 그림과 5000번의 모의실험을 통하여 허용한계를 구하였다 그 결과 제안된 극단간 분포(Extreme Value Distribution)가 일일 최고기온을 잘 설명하고 있음을 확인할 수 있었다. 논문에서 나타난 실제 데이터의 그림은 서울의 1월과 6월을 중심으로 하였고, 대상지역의 2006년과 100년 후 2105년의 평균기온과, 제 안된 극단값 분포에 의해 95% 신뢰구간하에서 일일 최고기온의 평균 상한값을 예측하였다.