A COMPARATIVE EVALUATION OF THE ESTIMATORS OF THE 2-PARAMETER GENERALIZED PARETO DISTRIBUTION

Singh, V.P.,Ahmad, M.,Sherif, M.M. Korea Water Resources Association 2003 Water engineering research Vol.4 No.3

Parameters and quantiles of the 2-parameter generalized Pareto distribution were estimated using the methods of regular moments, modified moments, probability weighted moments, linear moments, maximum likelihood, and entropy for Monte Carlo-generated samples. The performance of these seven estimators was statistically compared, with the objective of identifying the most robust estimator. It was found that in general the methods of probability-weighted moments and L-moments performed better than the methods of maximum likelihood estimation, moments and entropy, especially for smaller values of the coefficient of variation and probability of exceedance.

한국 주식 수익률에 대한 Extreme 분포의 적용 가능성에 관하여

김명석(Myung Suk Kim) 한국경영과학회 2007 經營 科學 Vol.24 No.2

Weekly minima of daily log returns of Korean composite stock price index 200 and its five industry-based business divisions over the period from January 1990 to December 2005 are fitted using two block-based extreme distributions;Generalized Extreme Value (GEV) and Generalized Logistic (GLO). Parameters are estimated using the probability weighted moments. Applicability of two distributions is investigated using the Monte Carlo simulation based empirical p-values of Anderson Darling test. Our empirical results indicate that both the GLO and GEV models seem to be comparably applicable to the weekly minima. These findings are against the evidences in Gettinby et al. [7], who claimed that the GEV model was not valid in many cases, and supported the significant superiority of the GLO model.

우리나라의 연 강수량, 계절 강수량 및 월 강수량의 확률분포형 결정

김동엽 ( Dong Yeob Kim ),이상호 ( Sang Ho Lee ),홍영주 ( Young Joo Hong ),이은재 ( Eun Jai Lee ),임상준 ( Sang Jun Im ) 한국농림기상학회 2010 한국농림기상학회지 Vol.12 No.2

본 연구의 목적은 우리나라의 연 강수량, 계절 강수량 그리고 월 강수량의 최적 확률분포형을 선정하는 것이다. 이를 위해서 전국 32개의 강우 관측소에서 얻은 자료에 대하여 L-모멘트 비 다이어그램과 평균가중거리 값을 이용하여 각 강수량별 최적 확률분포를 산정하였으며, 최종적으로 선정된 최적 확률분포형을 관측 지점별로 적합도 검정을 실시하였다. 그 결과, 연강수량에서는 3변수 Weibull 분포(W3), 봄과 가을에는 3변수 대수정규분포(LN3), 여름과 겨울에는 일반화된 극치분포(GEV)가 관측값에 가장 잘 적합하는 것으로 나타났다. 또한, 월 강수량에서는 1월은 LN3, 2월과 7월은 W3, 3월은 2변수 Weibull 분포(W2), 4월, 9월, 10월, 11월은 일반화된 Pareto 분포(GPA), 5월과 6월은 GEV, 그리고 8월과 12월은 log-Pearson typeIII 분포(LP3)가 가장 잘 적합하였다. 하지만, 최적 확률분포형의 지점별 적합도 검정의 결과, 1월, 4월, 9월, 10월, 11월의 GPA와 LN3에 대한 기각율이 확률분포의 매개변수 추정에서의 오류와 상대적으로 높은AWD 값으로 인하여 매우 높게 나타났다. 한편, 23개관측소의 자료를 추가하여 분석해본 결과 기존의 32개의 관측소 자료를 이용한 것과 큰 차이를 나타내지 않았다. 종합적으로 보다 적합한 확률분포형을 선정하기 위해서는 더 장기간의 표본자료를 이용한 추가적인 연구가 필요할 것으로 판단된다. The objective of this study was to determine the best probability distributions of annual, seasonal and monthly precipitation in Korea. Data observed at 32 stations in Korea were analyzed using the Lmoment ratio diagram and the average weighted distance (AWD) to identify the best probability distributions of each precipitation. The probability distribution was best represented by 3-parameter Weibull distribution (W3) for the annual precipitation, 3-parameter lognormal distribution (LN3) for spring and autumn seasons, and generalized extreme value distribution (GEV) for summer and winter seasons. The best probability distribution models for monthly precipitation were LN3 for January, W3 for February and July, 2-parameter Weibull distribution (W2) for March, generalized Pareto distribution (GPA) for April, September, October and November, GEV for May and June, and log-Pearson type III (LP3) for August and December. However, from the goodness-of-fit test for the best probability distributions of the best fit, GPA for April, September, October and November, and LN3 for January showed considerably high reject rates due to computational errors in estimation of the probability distribution parameters and relatively higher AWD values. Meanwhile, analyses using data from 55 stations including additional 23 stations indicated insignificant differences to those using original data. Further studies using more long-term data are needed to identify more optimal probability distributions for each precipitation.

LH-Moments of Some Distributions Useful in Hydrology

Murshed, Md. Sharwar,Park, Byung-Jun,Jeong, Bo-Yoon,Park, Jeong-Soo The Korean Statistical Society 2009 Communications for statistical applications and me Vol.16 No.4

It is already known from the previous study that flood seems to have heavier tail. Therefore, to make prediction of future extreme label, some agreement of tail behavior of extreme data is highly required. The LH-moments estimation method, the generalized form of L-moments is an useful method of characterizing the upper part of the distribution. LH-moments are based on linear combination of higher order statistics. In this study, we have formulated LH-moments of five distributions useful in hydrology such as, two types of three parameter kappa distributions, beta-${\kappa}$ distribution, beta-p distribution and a generalized Gumbel distribution. Using LH-moments reduces the undue influences that small sample may have on the estimation of large return period events.

Estimation for scale parameter of type-I extreme value distribution

Byung Jin Choi 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.2

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

Estimation for scale parameter of type-I extreme value distribution

최병진 한국데이터정보과학회 2015 한국데이터정보과학회지 Vol.26 No.2

In a various range of applications including hydrology, the type-I extreme valuedistribution has been extensively used as a probabilistic model for analyzing extremeevents. In this paper, we introduce methods for estimating the scale parameter ofthe type-I extreme value distribution. A simulation study is performed to comparethe estimators in terms of mean-squared error and bias, and the obtained results areprovided.

Estimation for scale parameter of type-I extreme value distribution

Choi, Byungjin The Korean Data and Information Science Society 2015 한국데이터정보과학회지 Vol.26 No.2

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.

부산지역 확률강수량 결정에 따른 재현기간 및 분포도 분석

임윤규,문윤섭,김진석,송상근,황용식 한국지구과학회 2012 한국지구과학회지 Vol.33 No.1

In this study, a statistical estimation of probable precipitation and an analysis of its return period in Busan were performed using long-term precipitation data (1973-2007) collected from the Busan Regional Meteorological Administration. These analyses were based on the method of probability weighted moments for parameter estimation, the goodness-of-fit test of chi-square (χ2) and the probability plot correlation coefficient (PPCC), and the generalized logistics (GLO) for optimum probability distribution. Moreover, the spatial distributions with the determination of probable precipitation were also investigated using precipitation data observed at 15 Automatic Weather Stations (AWS) in the target area. The return periods for the probable precipitation of 245.2 ㎜/6hr and 280.6 ㎜/6hr with GLO distributions in Busan were estimated to be about 100 and 200 years, respectively. In addition, the high probable precipitation for 1-hour, 3-hour, 6-hour, and 12-hour durations was mostly distributed around Dongrae-gu site, all coastal sites in Busan, Busanjin and Yangsan sites, and the southeastern coastal and Ungsang sites, respectively. 본 연구에서는 부산지방기상청 장기 강수량 자료(1973-2007)를 이용하여 부산지역 확률강수량 및 이에 따른 재현기간을 산정하였다. 확률강수량 산정에 있어서 확률가중모멘트법을 이용하여 매개변수를 추정하였고, χ2 및 PPCC 검정을 통해 적합성분석을 실시하였다. 분석결과 최적의 확률분포형으로 GLO 모형을 채택하였다. 또한 AWS 자료를 이용하여 부산지역 확률강수량 분포도를 작성하였다. 6시간 지속강수량에 있어서 245.2 ㎜의 강수량이 100년 마다 발생할 수 있으며, 280.6 ㎜가 200년에 한번 정도 나타날 수 있다. 확률강수량 분포도 결과 1시간 지속강수일 경우 동래구에서 높은 값을 가지며, 3시간 지속강수는 부산연안 전반에 걸쳐 높게 나타나고 있다. 6시간 지속강수량일 경우는 부산진과 양산일대에서 높은 값을 나타내며 12시간 지속강수의 경우 남동연안지역과 웅상 일대에서 높은 값을 보이는 특징이 나타났다.

Monte Carlo 모의를 이용한 지점 간 확률가중모멘트의 교차상관관계

신홍준,정영훈,허준행 한국수자원학회 2009 한국수자원학회논문집 Vol.42 No.3

본 연구에서는 지점 간 확률가중모멘트의 교차상관관계를 구하기 위해 Monte Carlo 모의를 이용하여 이를 지점간 표본자료의 교차상관성에 대한 관계식으로 확장하여 근사값을 구하고자 하였다. 모의실험 결과 각각의 확률가중 모멘트간 교차상관계수는 지점 간 표본자료의 교차상관계수와 자료크기가 동일하고 동시간 자료일 경우 기울기 1인 선형관계를 보이며, 자료크기에 따른 동시간 자료의 비율이 작아질수록 선형적인 관계는 점점 약해지게 된다. 따라서 자료크기에 따 In this study, cross correlations among sample data at each site are calculated to obtain the asymptotic cross correlations among probability weighted moments at each site using Monte Carlo simulation. As a result, the relations between the asymptotic cro

Jackknife empirical likelihood based inference for probability weighted moments

Bhati Deepesh,Kattumannil Sudheesh K.,Sreelakshmi N. 한국통계학회 2021 Journal of the Korean Statistical Society Vol.50 No.1

We discuss jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) based inference for fnding confdence intervals for probability weighted moment (PWM). We obtain the asymptotic distribution of the JEL ratio and AJEL ratio statistics. We compare the performance of the proposed confdence intervals with recently developed methods in terms of coverage probability and average width. We also develop JEL and AJEL based tests for PWM and study its properties. Finally we illustrate our method using rainfall data of Indian states.