• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• The Korean Journal of Financial Management
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• v.22 no.1
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• pp.119-146
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• 2005

This study applies extreme value theory to get extreme value-VAR for Korean Stock market and showed the usefulness of the approach. Block maxima model and POT model were used as extreme value models and tested which model was more appropriate through back testing. It was shown that the block maxima model was unstable as the variation of the estimate was very large depending on the confidence level and the magnitude of the estimates depended largely on the block size. This shows that block maxima model was not appropriate for Korean Stock market. On the other hand POT model was relatively stable even though extreme value VAR depended on the selection of the critical value. Back test also showed VAR showed a better result than delta VAR above 97.5% confidence level. POT model performs better the higher the confidence level, which suggests that POT model is useful as a risk management tool especially for VAR estimates with a confidence level higher than 99%. This study picks up the right tail and left tail of the return distribution and estimates the EVT-VAR for each, which reflects the asymmetry of the return distribution of the Korean Stock market.

• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.803-812
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• 2009

The application of extreme value theory to financial data is a fairly recent innovation. The classical annual maximum method is to fit the generalized extreme value distribution to the annual maxima of a data series. An alterative modern method, the so-called threshold method, is to fit the generalized Pareto distribution to the excesses over a high threshold from the data series. A more substantial variant is to take the point-process viewpoint of high-level exceedances. That is, the exceedance times and excess values of a high threshold are viewed as a two-dimensional point process whose limiting form is a non-homogeneous Poisson process. In this paper, we apply the two-dimensional non-homogeneous Poisson process model to daily losses, daily negative log-returns, in the data series of KBW/USD exchange rate, collected from January 4th, 1982 until December 31 st, 2008. The main question is how to estimate extreme quantiles of losses such as the 10-year or 50-year return level.

• Journal of Electrical Engineering and Technology
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• v.11 no.5
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• pp.1093-1099
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• 2016

• Communications for Statistical Applications and Methods
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• v.22 no.6
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• pp.647-653
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• 2015

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

• Journal of Communications and Networks
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• v.15 no.6
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• pp.576-580
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• 2013

In this paper, we investigate the capacity of a multipoint-to-point cognitive radio network. In existing works, the asymptotic capacity is only obtained in the high peak power region at secondary transmitter (ST) or obtained without considering the interference from primary transmitter (PT) for easy analysis. Here, we analyze the asymptotic capacity by considering an arbitrary peak power at the ST and the interference from the PT based on extreme value theory. Simulation results show that our approximated capacity is well-matched to the exact capacity. Furthermore, the scaling law of our capacity is found to be double logarithm of the number of secondary users.

• The Korean Journal of Applied Statistics
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• v.29 no.4
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• pp.753-771
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• 2016

Value at Risk (VaR) is widely used as an important tool for risk management of financial institutions. In this paper we discuss estimation and back testing for VaR of the portfolio composed of KOSPI, Dow Jones, Shanghai, Nikkei indexes. The copula functions are adopted to construct the multivariate distributions of portfolio components from marginal distributions that combine extreme value theory and GARCH models. Volatility models with t distribution of the error terms using Gaussian, t, Clayton and Frank copula functions are shown to be more appropriate than the other models, in particular the model using the Frank copula is shown to be the best.

• Communications for Statistical Applications and Methods
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• v.29 no.3
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• pp.319-331
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• 2022

In this paper, we develop a new statistical model to forecast the PM_2.5 level in Seoul, South Korea. The proposed model is based on the extreme quantile regression model with lasso penalty. Various meteorological variables and air pollution variables are considered as predictors in the regression model, and the lasso quantile regression performs variable selection and solves the multicollinearity problem. The final prediction model is obtained by combining various extreme lasso quantile regression estimators and we construct a binary classifier based on the model. Prediction performance is evaluated through the statistical measures of the performance of a binary classification test. We observe that the proposed method works better compared to the other classification methods, and predicts 'very bad' cases of the PM_2.5 level well.

• 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.

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