• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.734-737
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• 2004

When the margin level is set relatively low, margin violation probability increases and the default probability of the futures market rises. On the other hand, if the margin level is set high, the margin violation probability decreases, but the futures market becomes less attractive to hedgers as the investor's opportunity cost increases. In this paper, we investigate whether the movement of KOSPI200(Korea Composite Stock Price Index 200) futures daily prices can be modeled with the extreme value theory. Base on this investigation, we examine the validity of the margin level set by the extreme value theory. Computational results are presented to compare the extreme value distribution and the empirical distribution of margin violation in KOSPI200. Some observations and implications drawn from the computational experiment are also discussed.

• Journal of the Korean Data and Information Science Society
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• v.25 no.4
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• pp.903-914
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• 2014

The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as a suitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modified empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

• 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 Korea Water Resources Association
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• v.50 no.3
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• pp.211-221
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• 2017

In statistical hydrology, various extreme distributions such as the generalized extreme value (GEV), generalized logistic (GLO) and Gumbel (GUM) models have been widely used to analyze the extreme events. In the case of rainfall events in South Korea, the GEV and Gumbel distributions are known to be appropriate among various extreme distribution models. However, the proper probability distribution model may be different depending on the type of extreme events, rainfall duration, region, and statistical characteristics of extreme events. In this regard, it is necessary to apply a wide range of statistical properties that can be represented by the distribution model because it has two shape parameters. In this study, the statistical applicability of rainfall data is analyzed using the Burr XII distribution and the dimensionless L-moment ratio for 620 stations in South Korea. For this purpose, L-skewness and L-kurtosis of the Burr XII distribution are derived and L-moment ratio diagram is drawn and then the applicability of 620 stations was analyzed. As a result, it is found that the Burr XII distribution for the stations of the Han River basin in which L-skewness is relatively larger than L-kurtosis is appropriate, It is possibility of replacing the distribution of commonly used Gumbel or GEV distributions. Therefore, the Burr XII model can be replaced as an appropriate probability model in this basin.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.6B
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• pp.623-629
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• 2009

In this research, the process of developing software products to users in transfer by considering the warranty period to determine the timing of the release period is a comparative study of models. For the results of demonstration, exponential software reliability model increases the warranty period, the higher the initial period, but shows almost a similar release. In contrast, the optimal release time of imperfect debugging software reliability model, lower the initial warranty period, but the pattern is expected to rise slightly larger. The proposed model, extreme value distribution model, pattern of the optimal release time gradually increase, have a form that can be drawn. These research results through, warranty period and release the software developers understand the relationship between the optimal time for software development by using advance information could do is feed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.2
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• pp.223-230
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• 2012

The strength of brittle material has commonly been characterized by a normal distribution or Weibull distribution, but it may fit the gamma distribution for some material. The use of an extreme value distribution is proper when the largest values of a set of stresses dominate the failure of the material. This paper presents a formula for reliability estimation based on stress-strength interference theory that is applicable when the strength of material is distributed like a gamma distribution and the stress is distributed like an extreme value distribution. We verified the validity of the equation for the reliability estimation by examining the relationships among the factor of safety, the coefficient of variation, and the reliability. The required minimum factor of safety and the highest allowable coefficient of variation of stress can be estimated by choosing an objective reliability and estimating the reliabilities obtained for various factors of safety and coefficients of variation.

• Korean Management Science Review
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• v.24 no.2
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• pp.115-126
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• 2007

Weekly minima of daily log returns of Korean composite stock price index 200 and its five industry-based business divisions over the period from January 1990 to December 2005 are fitted using two block-based extreme distributions: Generalized Extreme Value(GEV) and Generalized Logistic(GLO). Parameters are estimated using the probability weighted moments. Applicability of two distributions is investigated using the Monte Carlo simulation based empirical p-values of Anderson Darling test. Our empirical results indicate that both the GLO and GEV models seem to be comparably applicable to the weekly minima. These findings are against the evidences in Gettinby et al.[7], who claimed that the GEV model was not valid in many cases, and supported the significant superiority of the GLO model.

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

• The Korean Journal of Applied Statistics
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• v.20 no.1
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• pp.1-9
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• 2007

This investigation on the change of the daily maxima temperature in Seoul, Daegu, Chunchen, Youngchen was triggered by news items such as the earth is getting warmer and a recent news item that said that Korea is getting warmer due to this climatic change. A statistical analysis on the daily maxima for June over this period in Seoul revealed a positive trend of 1.1190 centigrade over the 45 years, a change of 0.0249 degrees annually. Due to the large variation on these maximum temperatures, one can raise the question on the significance of this increase. To check the goodness of fit of the proposed extreme value model, we shown a Q-Q plot of the observed quantiles against the simulated quantiles and a probability plot. And we calculated statistics each month and a tolerance limit. This is tested through simulating a large number of similar datasets from an Extreme Value distribution which described the observed data very well. Only 0.02% of the simulated datasets showed an increase of this degrees or larger, meaning that the probability is very low for such an event to occur.