• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.313-336
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• 1996

In this paper we consider weak convergence of some rescaled transi-tion probabilities of a real-valued, k-th order (k $\geq$ 1) stationary Markov chain. Under the assumption that the joint distribution of K + 1 consecutive variables belongs to the domain of attraction of a multivariate extreme value distribution, the paper gives a sufficient condition for the weak convergence and characterizes the limiting distribution via the multivariate extreme value distribution.

• 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 applied mathematics & informatics
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• v.18 no.1_2
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• pp.247-259
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• 2005

Necessary and sufficient conditions, under which there exists (at least) a sequence of vectors of real numbers for which the distribution function (d.f.) of any vector of extreme order statistics converges to a non-degenerate limit, are derived. The interesting thing is that these conditions solely depend on the univariate marginals. Moreover, the limit splits into the product of the limit univariate marginals if all the bivariate marginals of the trivariate d.f., from which the sample is drawn, is of negative quadrant dependent random variables (r.v.'s). Finally, all these results are stated for the multivariate extremes with arbitrary dimensions.

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

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

• 한국방재학회:학술대회논문집
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• 2008.02a
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• pp.653-655
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• 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
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• v.23 no.2
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• pp.119-129
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• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.1B
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• pp.13-20
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• 2011

The spatio-temporal pattern in precipitation is a significant element in defining characteristics of precipitation. In this study, a new scheme on regionalization utilizing temporal information was introduced on the basis of existing approaches that is mainly based on simple moments of data and geographical information. Given the identified spatio-temporal pattern, this study was extended to characterize regional pattern of annual maximum rainfall over Korea. We have used circular statistics to characterize the temporal distribution on the precipitation, and the circular statistics allow us to effectively assess changes in timing of the extreme rainfall in detail. In this study, a modified K-means method was incorporated with derived temporal characteristics of extreme rainfall in order to better characterize hydrologic pattern for regional frequency analysis. The extreme rainfall was reasonably separated into five categories that considered most attributes in both quantitative and temporal changes in extremes. The results showed that the proposed approach is a promising approach for regionalization in term of physical understanding of extreme rainfall.

• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.101-114
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• 2012

In car insurance, the loss ratio is the ratio of total losses paid out in claims divided by the total earned premiums. In order to minimize the loss to the insurance company, estimating extreme quantiles of loss ratio distribution is necessary because the loss ratio has essential prot and loss information. Like other types of insurance related datasets, the distribution of the loss ratio has heavy-tailed distribution. The Peaks over Threshold(POT) and the Hill estimator are commonly used to estimate extreme quantiles for heavy-tailed distribution. This article compares and analyzes the performances of various kinds of parameter estimating methods by using a simulation and the real loss ratio of car insurance data. In addition, we estimate extreme quantiles using the Hill estimator. As a result, the simulation and the loss ratio data applications demonstrate that the POT method estimates quantiles more accurately than the Hill estimation method in most cases. Moreover, MLE, Zhang, NLS-2 methods show the best performances among the methods of the GPD parameters estimation.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.847-858
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• 2015

Deep-sea fishery in the Antarctic Ocean has been actively progressed by the developed countries including Korea. In order to prevent the environmental destruction of the Antarctic Ocean, related countries have established the Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR) and have monitored any illegal unreported or unregulated fishing. Fishing of tooth fish, an expensive fish, in the Antarctic Ocean has increased recently and high catches per unit effort (CPUE) of fishing boats, which is suspicious for an illegal activity, have been frequently reported. The data of CPUEs in a fishing area of the Antarctic Ocean often show an extreme Distribution or a mixture of two extreme distributions. This paper proposes an algorithm to detect an outlier of CPUEs by using the mixture of two extreme distributions. The parameters of the mixture distribution are estimated by the EM algorithm. Log likelihood value and posterior probabilities are used to detect an outlier. Experiments show that the proposed algorithm to detect outlier of the data can be adopted instead of simple criteria such as a CPUE is greater than 1.