• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.247-259
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• 2005

Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.

• Journal of the Korean Statistical Society
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• 제32권4호
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• pp.313-335
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• 2003

Hourly ozone data are available for 73 stations in South Korea from January, 1988 to August, 1998. We are interested in detecting trends in both the mean levels and the extremes of ozone, and in determining how these trends vary over the country. The latter aspect means that we also have to understand the spatial dependence of ozone. In this connection, therefore, we examine in this paper the following features: determining trends in mean ozone levels at individual stations and combination across stations; determining trends in extreme ozone levels at individual stations and combination across stations; spatial modeling of trends in mean and extreme ozone levels.

• 대한수학회보
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• 제49권3호
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• pp.495-510
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• 2012

Let $X_1$, $X_2$,${\ldots}$, $X_n$ be a sequence of independent and identically distributed random variables with common distribution function $F$. Convergence rates for the moments of extremes are studied by virtue of second order regularly conditions. A unified treatment is also considered under second order von Mises conditions. Some examples are given to illustrate the results.

• Wind and Structures
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• 제4권4호
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• pp.353-366
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• 2001

With respect to serviceability, antenna masts should be designed so that wind-induced motion will not cause unacceptable lack of transmission for broadcasting users and wireless communication. For such antenna masts with directional radio transmission the serviceability limit state is predominantly governed by the tolerable change of the broadcasting angle of the mounted antenna assembly and therefore by the tip distortion of the mast. In this paper it will be shown that refinements of the present state of design of antenna masts are possible by using the statistics of extremes applied to extreme wind situations and by consideration of the statistical and reliability requirements given by the operator such as frequency and return period of passing the serviceability limit.

• Communications for Statistical Applications and Methods
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• 제22권3호
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• pp.277-283
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• 2015

Pickands constant $H_{\alpha}$ appears in the classical result about tail probabilities of the extremes of Gaussian processes and there exist several different representations of Pickands constant. However, the exact value of $H_{\alpha}$ is unknown except for two special Gaussian processes. Significant effort has been made to find numerical approximations of $H_{\alpha}$. In this paper, we attempt to compute numerically $H_{\alpha}$ based on its representation derived by $H{\ddot{u}}sler$ (1999) and Albin and Choi (2010). Our estimates are compared with the often quoted conjecture $H_{\alpha}=1/{\Gamma}(1/{\alpha})$ for 0 < ${\alpha}$ ${\leq}$ 2. This conjecture does not seem compatible with our simulation result for 1 < ${\alpha}$ < 2, which is also recently observed by Dieker and Yakir (2014) who devised a reliable algorithm to estimate these constants along with a detailed error analysis.

• 응용통계연구
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• 제27권4호
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• pp.655-665
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• 2014

폭염, 폭우와 가뭄 등과 같은 이상 기후 현상에 대한 적절한 대응이 최근 많이 요구되고 있다. 이상 기후 현상을 분석하기 위해 극단값 분석 기법을 적용할 수 있는데, 본 논문은에서는 한국의 여름철 강수량 자료(1973년부터 2012년까지의 5월부터 9월)를 분계점 초과값 모형으로 분석해보았다. 분계점은 한국의 기상관측소들을 5개의 군집으로 나누어, 각 군집별로 지리 정보와 시간을 공변량으로 하는 분위수 회귀 방법을 통하여 추정하였다. Northrop과 Jonathan (2011)과 같이 극단값들이 시공간적으로 독립이라고 가정하고 분석한 후, 추정오차와 검정 과정에 공간 종속성을 반영하였다.

• 대한수학회보
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• 제53권5호
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• pp.1549-1566
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• 2016

Denote $M_n$ the maximum of n independent and identically distributed variables from the generalized short-tailed symmetric distribution. This paper shows the pointwise convergence rate of the distribution of $M_n$ to exp($\exp(-e^{-x})$) and the supremum-metric-based convergence rate as well.

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

• Journal of applied mathematics & informatics
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• 제20권1_2호
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• pp.225-238
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• 2006

Generalized order statistics (gos) introduced by Kamps [8] as a unified approach to several models of order random variables (rv's), e.g., (ordinary) order statistics (oos), records, sequential order statistics (sos). In a wide subclass of gos, included oos and sos, the possible limit distribution functions (df's) of the maximum gos are obtained in Nasri-Roudsari [10]. In this paper, for this subclass, as the df of the suitably normalized extreme gos converges on an interval [c, d] to one of possible limit df's of the extreme gos, the continuation of this (weak) convergence on the whole real line to this limit df is proved.

• Communications for Statistical Applications and Methods
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• 제27권2호
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• pp.163-175
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• 2020

We consider a wide class of general weakly-dependent processes, called ψ-weak dependence, which unify almost all weak dependence structures of interest found in statistics under natural conditions on process parameters, such as mixing, association, Bernoulli shifts, and Markovian sequences. For detecting the tail behavior of the weakly dependent processes, change point tests are developed by means of cumulative sum (CUSUM) statistics with the empirical distribution functions of sample extremes. The null limiting distribution is established as a Brownian bridge. Its proof is based on the ψ-weak dependence structure and the existence of the phantom distribution function of stationary weakly-dependent processes. A Monte-Carlo study is conducted to see the performance of sizes and powers of the CUSUM tests in GARCH(1, 1) models; in addition, real data applications are given with log-returns of financial data such as the Korean stock price index.