• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.289-297
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• 1997

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

• Journal of the Korean Statistical Society
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• 제36권1호
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• pp.93-109
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• 2007

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

• 대한조선학회논문집
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• 제33권1호
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• pp.145-152
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• 1996

본 연구에서는 해상 구조물에 작용하는 설계 파랑 하중을 산정하기 위하여 해상에서 관측되거나 또는 예측된 파랑 자료를 사용하여 해상 구조물의 설계 생존 기간 동안 만나게 될 극한 설계파를 산정하는 기법을 개발하였다. 주어진 파랑 자료에 Order Statistics와 Monte Carlo Simulation 기법을 적용하여 가장 알맞은 파랑 자료의 극한 분포식을 선택하여 이 분포식으로부터 원하는 회귀 주기에 해당하는 극한 설계파를 결정하고 결정된 극한 설계 파고의 불확실성에 대한 범위를 설정함으로서 설계 파고의 여유를 줄 수 있다. 이와 같은 기법을 우리나라 남해안의 1938년부터 1987년까지 태풍에 의한 파랑 자료에 적용하여 극한 설계파를 산정하는 예를 보였다. 이상과 같은 방법을 이용함으로서 대형 해양 구조물을 설계함에 있어 극한 하중 상태를 산정할 수 있는 정보를 설계 초기 단계에 제공할 수 있으며 해당 구조물의 주요 요목, 구조 등의 설계 인자들을 산정할 수 있다.

• 응용통계연구
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• 제26권4호
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• pp.595-610
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• 2013

범주형 자료에서 순서화된 대립가설을 검정하는 경우는 의학 사회학 경영학 등 다양한 응용분야에서 발생한다. 이러한 검정 방법은 대부분 대표본이론에 근거하여 개발되었다. 하지만 표본크기가 작거나 표본크기가 매우 불균등한 경우 대표본이론에 근거한 검정방법의 제 1종 오류 확률은 목표로 하는 5%와 멀어지는 경우가 많이 발생한다. 본 논문에서는 범주형 자료에서 순서화된 대립가설을 검정하는 경우 표본크기가 작거나 표본크기가 매우 불균등한 경우에 사용될 수 있는 정확검정방법을 소개하고 이에 대한 검정력 및 정확 p-value를 제시할 것이다.

• 한국환경과학회지
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• 제19권10호
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• pp.1237-1246
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• 2010

This paper aims to analyze the perception of university students for the extreme heat watch warning and suggest the usefulness of special weather reports. For this, we have made up a descriptive questionnaires including the perception, mass media, usefulness and satisfaction of special weather report. Using the SPSS 17.0 program, descriptive statistics, t-test, ANOVA and Scheffe test were used to analyze the collected data. The result are as follows; The perception of extreme heat watch warning was some low as 59.1 percentile, we think it needs education and public relations about the extreme heat watch warning. The usefulness of special weather report was 66.6 percentile and of girl students of university that was educated about health care was higher than one of boy students of university, it needs continuous education of these students in order to upgrade satisfaction of special report and mitigate the hazard of extreme heat according to climate change. The main media to get the meteorological information of university undergraduate students were TV and Internet, it needed education and development of new contents. From these findings, suggestions are presented to help improve the extreme heat watch warning.

• 대한기계학회논문집A
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• 제26권9호
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• pp.1746-1752
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• 2002

Fatigue fracture in machine components is produced by surface micro-crack from stress concentration area such as notch and material defect. It is difficult to predict the remaining fatigue lift of mechanical components because the surface micro-crack on critical area initiates and grows with statistical distribution. Plane bending fatigue tests were carried out on the plain specimen of Al 2024-T3 and the initiation and growth behavior of surface micro cracks were observed. The statistical distribution of surface length of multiple micro cracks and their maximum length were investigated. The maximum surface crack length distributions were analyzed on the basis of the statistics of extremes in order to examine the prediction of remaining life.

• 응용통계연구
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• 제25권5호
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• pp.757-773
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• 2012

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.

• Communications for Statistical Applications and Methods
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• 제31권4호
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• pp.459-466
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• 2024

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

• International Journal of Reliability and Applications
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• 제8권2호
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• pp.153-173
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• 2007

Wood-plastic composites (WPC) are gaining market share in the building industry because of durability/maintenance advantages of WPC over traditional wood products and because of the removal of chromated copper arsenate (CCA) pressure-treated wood from the market. In order to ensure continued market share growth, WPC manufacturers need greater focus on reliability, quality, and cost. The reliability methods outlined in this paper can be used to improve the quality of WPC and lower manufacturing costs by reducing raw material inputs and minimizing WPC waste. Statistical methods are described for analyzing stiffness (tangent modulus of elasticity: MOE) and flexural strength (modulus of rupture: MOR) test results on sampled WPC panels. Descriptive statistics, graphs, and reliability plots from these test data are presented and interpreted. Sources of variability in the MOE and MOR of WPC are suggested. The methods outlined may directly benefit WPC manufacturers through a better understanding of strength and stiffness measures, which can lead to process improvements and, ultimately, a superior WPC product with improved reliability, thereby creating greater customer satisfaction.

• 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.