• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
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• 2006.11a
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• pp.367-372
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• 2006

If the sea is narrowband, the Rayleigh distribution introduced by Longuet-Higgins can be used for the individual wave height distribution. However the Rayleigh distribution over-predicts the probability of high waves. Longuet-Higgins introduced alternative form of the Rayleigh distribution with an empirical constant. The wave height distribution can be fitted well by one parameter Rayleigh distribution with a proper choice of the empirical constant. The empirical constant is the ratio of the significant wave height based the time domain analysis and the spectral analysis. Here we examine wave data which contain extreme waves. Once again we confirmed that extreme wave height distribution can be modelled well by a modified Rayleigh distribution.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.833-845
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• 2011

This paper conducts a statistical analysis of extreme values for both daily log-returns and daily negative log-returns, which are computed using a collection of KOSPI data from January 3, 1998 to August 31, 2011. The Poisson-GPD model is used as a statistical analysis model for extreme values and the maximum likelihood method is applied for the estimation of parameters and extreme quantiles. To the Poisson-GPD model is also added the Bayesian method that assumes the usual noninformative prior distribution for the parameters, where the Markov chain Monte Carlo method is applied for the estimation of parameters and extreme quantiles. According to this analysis, both the maximum likelihood method and the Bayesian method form the same conclusion that the distribution of the log-returns has a shorter right tail than the normal distribution, but that the distribution of the negative log-returns has a heavier right tail than the normal distribution. An advantage of using the Bayesian method in extreme value analysis is that there is nothing to worry about the classical asymptotic properties of the maximum likelihood estimators even when the regularity conditions are not satisfied, and that in prediction it is effective to reflect the uncertainties from both the parameters and a future observation.

• Journal of the Korean Data and Information Science Society
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• v.15 no.3
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• pp.593-603
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• 2004

We consider the problem of estimating the scale parameter of the Weibull distribution based on multiply Type-II censored samples. We propose two estimators by using the approximate maximum likelihood estimation method for Weibull and extreme value distributions. The proposed estimators are compared in the sense of the mean squared error.

• Journal of Advanced Marine Engineering and Technology
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• v.39 no.8
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• pp.828-832
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• 2015

This study is conducted for the evaluation of corrosion and lifetime prediction of fire extinguishing pipelines in residential buildings. The fire extinguishing pipeline is made of carbon steel. Twenty-four samples were selected among all the fire extinguishing pipelines in a building; the selection was based on specimenspositions, pipeline diameters, and pipeline thickness. Analysis was conducted by using the results of visual inspection, electrochemical potentiodynamic anodic polarization test, pitting depth measurements, and extreme value statistics with the Gumbel distribution. The maximum pitting depth and remaining life were statistically predicted using extreme value statistics. During visual inspection, pitting corrosion was observed in several samples. In addition, extreme value statistics demonstrated that there were several pipelines that were very sensitive to pitting corrosion. However, the pitting corrosion was not critical in all the pipelines; thus, it was necessary to change only those pipelines that were severely corroded.

• Journal of the Korean Society for Marine Environment & Energy
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• v.1 no.2
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• pp.71-81
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• 1998

In this paper the statistical characteristics of the waves at Hong-do and Mara-do are examined. The wane scatter diagrams of H/sub s/ and T/sub z/ and H/sub 1/3/and T/sub 1/3/ at two locations are given and various statistical characteristics of the ocean waves are examined. If the sea is not narrowband, the modified Rayleigh distribution introduced by Longuet-Higgins can be used for the individual wave height distribution. However the modified Rayleigh distribution has not been widely used due to the inconvenience of determining the empirical constant. In this paper a simple method to determine the empirical constant for the modified Rayleigh distribution is proposed. Extreme waves based on the measured wave data are estimated. There is no significant difference depending on the distribution functions. However the estimations of the extreme waves from H/sub s/ and H/sub 1/3/ show considerable difference.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.15-27
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• 2018

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than $beta-{\kappa}$, Gumbel, and GEV distributions.

• The Journal of the Convergence on Culture Technology
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• v.8 no.1
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• pp.531-536
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• 2022

This paper compared the performance of the parametric method and the nonparametric method when estimating the distribution for the tail of the distribution with heavy tails. For the parametric method, the generalized extreme value distribution and the generalized Pareto distribution were used, and for the nonparametric method, the kernel density estimation method was applied. For comparison of the two approaches, the results of function estimation by applying the block maximum value model and the threshold excess model using daily fine dust public data for each observatory in Seoul from 2014 to 2018 are shown together. In addition, the area where high concentrations of fine dust will occur was predicted through the return level.

• Journal of the Korean Statistical Society
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• v.34 no.2
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• pp.125-140
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• 2005

In this paper, we consider the estimation of the correlation coefficient in the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) that was introduced by Al-Saleh and Al-Hadhrami (2003a). The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered under different settings. The obtained estimators are compared to their counterparts that are obtained based simple random sampling (SRS). It appears that the suggested estimators are more efficient

• Wind and Structures
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• v.9 no.3
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• pp.179-191
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• 2006

Parent wind data are often acknowledged to fit a Weibull probability distribution, implying that wind epoch maxima should fall into the domain of attraction of the Gumbel (Type I) extreme value distribution. However, observations of wind epoch maxima are not fitted well by this distribution and a Generalised Extreme Value (GEV) analysis leading to a Type III fit empirically appears to be better. Thus there is an apparent paradox. The reasons why advocates of the GEV approach seem to prefer it are briefly summarised. This paper gives a detailed analysis of the errors involved when the GEV is fitted to epoch maxima of Weibull origin. It is shown that the results in terms of the shape parameter are an artefact of these errors. The errors are unavoidable with the present sample sizes. If proper significance tests are applied, then the null hypothesis of a Type I fit, as predicted by theory, will almost always be retained. The GEV leads to an unacceptable ambiguity in defining design loads. For these reasons, it is concluded that the GEV approach does not seem to be a sensible option.

• New & Renewable Energy
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• v.20 no.2
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• pp.2-16
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• 2024

Various loads induced by marine environmental conditions, such as waves, currents, and wind, are crucial for the operation and viability of offshore wind power (OWP) systems. In particular, waves have a significant impact on the stress and fatigue load of offshore structures, and highly reliable design parameters should be derived through extreme value analysis (EVA) techniques. In this study, extreme wave analyses were conducted with various Weibull distribution models to determine the reliable design parameters of an OWP system suitable for the Ulsan area. Forty-three years of long-term hindcast data generated by a numerical wave model were adopted as the analyses data, and the least-squares method was used to estimate the parameters of the distribution function for EVA. The inverse first-order reliability method was employed as the EVA technique. The obtained results were compared among themselves under the assumption that the marginal probability distributions were 2p, 3p, and exponentiated Weibull distributions.