• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1441-1448
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• 2008

We propose the modified quantile-quantile (Q-Q) plot using the approximate maximum likelihood estimators and the modified normalized sample Lorenz curve (NSLC) plot for the extreme value distribution based on multiply Type-II censored samples. Using two example data sets, we picture the modified Q-Q plot and the modified NSLC plot.

• Journal of the Korean Data and Information Science Society
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• v.18 no.3
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• pp.817-826
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• 2007

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the location parameter in a generalized extreme value distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.643-653
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• 2014

In this paper, we propose some estimators for the extreme value distribution based on the interval method and mid-point approximation method from the progressive Type-I interval censored sample. Because log-likelihood function is a non-linear function, we use a Taylor series expansion to derive approximate likelihood equations. We compare the proposed estimators in terms of the mean squared error by using the Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• 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.

• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.249-273
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• 1996

This paper reviews and develops several statistical models for extreme values, based on threshold methodology. Extreme values of a time series are modeled in terms of tails which are defined as truncated forms of original variables, and Markov property is imposed on the tails. Tails of the generalized extreme value distribution and a multivariate extreme value distributively, of the tails of the series. These models are then applied to real ozone data series collected in the Chicago area. A major concern is given to detecting any possible trend in the extreme values.

• The Korean Journal of Applied Statistics
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• v.20 no.2
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• pp.291-311
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• 2007

With a series of unexpected huge losses in the financial markets around the world recently, especially in the insurance market with extreme loss cases such as catastrophes, there is an increasing demand for risk management for extreme loss exposures due to high unpredictability of those risks. For extreme risk management, to make a maximum use of the information concerning the tail part of a loss distribution, EVT(Extreme Value Theory) modelling nay be the best to analyze extreme values. The Extreme Value Theory is widely used in practice and, especially in financal markets, EVT modelling is getting popular to analyBe the effects of extreme risks. This study is to review the significance of the Extreme Value Theory in risk management and, focusing on analyzing insurer's risk capital, extreme risk is measured using the real fire loss data and insurer's specific amount of risk capital is figured out to buffer the extreme risk.

• Journal of the Korean Society of Safety
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• v.25 no.3
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• pp.112-117
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• 2010

This study presents a methodology to evaluate the driving safety of vehicles against localized high wind on the roads over the valleys or along the coasts. Risk level for vehicle accident is derived from the side slip caused by cross wind, and then safety criteria based on reliability for driving stability are defined. The level of safety is classified according to probability of exceeding against wind speed using the concept of extreme value statistics. To attain the safety level of vehicle on bridges, numerical simulations using Computational Fluid Dynamics(CFD) are performed. Based on this result, risk reduction and quality improvement is expected through analysis for each alternative in bridges design, construction and operation & maintenance stage with proposed process

• Journal of the Korean Statistical Society
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• v.32 no.4
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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.

• Journal of the Korean Data and Information Science Society
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• v.26 no.2
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• pp.535-545
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• 2015

In a various range of applications including hydrology, the type-I extreme value distribution has been extensively used as a probabilistic model for analyzing extreme events. In this paper, we introduce methods for estimating the scale parameter of the type-I extreme value distribution. A simulation study is performed to compare the estimators in terms of mean-squared error and bias, and the obtained results are provided.