• Communications for Statistical Applications and Methods
• /
• v.5 no.3
• /
• pp.855-868
• /
• 1998

For a random sample of size n from general linear model, $Y_i= heta(X_i)+varepsilon_i,;let Y_{in}$ denote the ith oder statistics of the Y sample values. The X-value associated with $Y_{in}$ is denoted by $X_{[in]}$ and is called the concomitant of ith order statistics. The estimator of the location of a maximum of a regression function, $ heta$($\chi$), was proposed by (equation omitted) and was found the convergence rate of it under certain weak assumptions on $ heta$. We will discuss the asymptotic distributions of both $ heta(X_{〔n-r+1〕}$) and (equation omitted) when r is fixed as nolongrightarrow$\infty$(i.e. extreme case) on the basis of the theorem of the concomitants of order statistics. And the will investigate the asymptotic behavior of Max｛$\theta$( $X_{〔n-r+1:n〕/}$ ), . , $\theta$( $X_{〔n:n〕}$)｝as an estimator for the peak of a regression function.

• Journal of Ocean Engineering and Technology
• /
• v.15 no.3
• /
• pp.20-27
• /
• 2001

After using the filtering method, wave parameters are calculated by the spectral analysis and wave by wave analysis. Extreme environments and higher wave characteristics int he Chujeon Sea are analyzed using the observed wave data. Higher wave has been intensely emphasized as an important environmental force parameter in several recent research works. The aims of this study are to summarize the distribution of extreme environment for wind waves, and to find occurrence probability of higher wave in Chujeon Sea. Ocean wave statistics varying with sea state are found to respond linearly to the spectral peakedness parameter Qp, mean run-length and Ursell number. Although the spreading of the field results is large, it may be concluded that the tendency of wave group formation depends on the spectral peakedness parameter Qp. Extreme wave is estimated to apply various model distribution functions by using the monthly maximum significant wave parameters which can be used to the design and analysis of coastal structures.

• Wind and Structures
• /
• v.9 no.3
• /
• pp.193-215
• /
• 2006

This paper presents an analysis of wind velocity measurements obtained from four ultrasonic anemometers arranged in a vertical formation. The anemometers were located in a rural environment with a view to providing detailed information on the flow statistics of the lower part of the atmospheric boundary layer, particularly for the extreme wind events that are important in loading calculations. The data is analysed using both conventional analysis and conditional sampling. The latter is combined with wavelet analysis in order to provide a detailed analysis of the energy/frequency relationship of the extreme events. The work presented in this paper suggests that on average the extreme events occur as a result of the superposition of two independent mechanisms - large scale events that scale on the atmospheric boundary layer thickness and small scale events a few tens of metres in size.

• The Korean Journal of Applied Statistics
• /
• v.33 no.1
• /
• pp.107-114
• /
• 2020

Extreme value distributions have often been used for the analysis (e.g., prediction of return level) of data which are observed from natural disaster. By the extreme value theory, the block maxima asymptotically follow the generalized extreme value distribution as sample size increases; however, this may not hold in a small sample case. For solving this problem, this paper proposes the use of a log-logistic (LLG) distribution whose validity is evaluated through goodness-of-fit test and model selection. The proposed method is illustrated with data from annual maximum earthquake magnitudes of China. Here, we present the predicted return level and confidence interval according to each return period using LLG distribution.

• Communications for Statistical Applications and Methods
• /
• v.16 no.4
• /
• pp.647-658
• /
• 2009

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.

• The Korean Journal of Applied Statistics
• /
• v.35 no.1
• /
• pp.119-129
• /
• 2022

In this paper, we predict the earthquake magnitudes which were recently occurred in Gyeongju and Pohang, using statistical methods based on historical data. For this purpose, we use the five-year block maximum data of 1392~1771 period, which has a relatively high annual density, among the historical earthquake magnitude data of the Chosun Dynasty. Then, we present the prediction and analysis of earthquake magnitudes for the return level over return period in the Chosun Dynasty using the extreme value theory based on the distribution of generalized extreme values (GEV). We use maximum likelihood estimation (MLE) and L-moments estimation for parameters of GEV distribution. In particular, this study also demonstrates via the goodness-of-fit tests that the GEV distribution can be an appropriate analytical model for these historical earthquake magnitude data.

• Honam Mathematical Journal
• /
• v.25 no.1
• /
• pp.117-127
• /
• 2003

In this note we perform an extreme point analysis on two natural definitions of negative quadrant dependence of three random variables and examine how different these two notions of dependence. We also characterize some special distributions which are both negatively lower orthant dependent and negatively upper orthant dependent.

• Communications for Statistical Applications and Methods
• /
• v.13 no.2
• /
• pp.389-407
• /
• 2006

Extreme value theory has been used widely in many areas of science and engineering to deal with the assessment of extreme events which are rare but have catastrophic consequences. The potential of extreme value theory has only been recognized recently in finance area. In this paper, we provide an overview of extreme value theory for estimating and assessing value at risk and expected shortfall which are the methods for modelling and measuring the extreme financial risks. We illustrate that the approach based on extreme value theory is very useful for estimating tail related risk measures through backtesting of an empirical data.

• 한국방재학회:학술대회논문집
• /
• 2008.02a
• /
• pp.653-655
• /
• 2008

In order to examine the influences by the extreme weather changes on the human physical conditions, we need to undertake human biometeorology research such as the assesment on the extreme heat's influences on human health. Most of the preceding studied have been found to be focused on the influences by extreme heat on the human body, they used statistics on the daily mortality. But thismethod estimate an indirectly influences by extreme heat on the human body. So, to be able to predict the possible directly influences by the extreme heat on the physical conditions. We measure thermal stress by extreme heat.

• Communications for Statistical Applications and Methods
• /
• v.23 no.2
• /
• 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.