• Journal of the Korean Data and Information Science Society
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• v.9 no.1
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• pp.47-56
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• 1998

Zero-Inflated Poisson models are mixed models of the Poisson and Bernoulli models. Recently Zero-Inflated Poisson distributions have been used frequently rather than previous Poisson distributions because the developement of industrial technology make few defects in manufacturing process. It is important that univariate Zero-Inflated Poisson distributions are extended to bivariate distributions to generalize the multivariate distributions. In this paper we proposed three types of the bivariate Zero-Inflated Poisson distributions and obtained these moments. We compared the three types of distributions by using the moments.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.1-19
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• 2021

Heavy tailed distributions are useful for modeling actuarial and financial risk management problems. Actuaries often search for finding distributions that provide the best fit to heavy tailed data sets. In the present work, we introduce a new class of heavy tailed distributions of a special sub-model of the proposed family, called a new extended alpha power transformed Weibull distribution, useful for modeling heavy tailed data sets. Mathematical properties along with certain characterizations of the proposed distribution are presented. Maximum likelihood estimates of the model parameters are obtained. A simulation study is provided to evaluate the performance of the maximum likelihood estimators. Actuarial measures such as Value at Risk and Tail Value at Risk are also calculated. Further, a simulation study based on the actuarial measures is done. Finally, an application of the proposed model to a heavy tailed data set is presented. The proposed distribution is compared with some well-known (i) two-parameter models, (ii) three-parameter models and (iii) four-parameter models.

• Journal of Environmental Science International
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• v.19 no.6
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• pp.689-701
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• 2010

The effects of high-resolution wind profiler (HWP) data on the wind distributions were evaluated in two different coastal areas during the study period (23-26 August, 2007), indicating weak-gradient flows. The analysis was performed using the Weather Research and Forecasting (WRF) model coupled with a three-dimensional variational (3DVAR) data assimilation system. For the comparison purpose, two coastal regions were selected as: a southwestern coastal (SWC) region characterized by a complex shoreline and a eastern coastal (EC) region surrounding a simple coastline and high mountains. The influence of data assimilation using the HWP data on the wind distributions in the SWC region was moderately higher than that of the EC region. In comparison between the wind speed and direction in the two coastal areas, the application of the HWP data contributed to improvement of the wind direction distribution in the SWC region and the wind strength in the EC region, respectively. This study suggests that the application of the HWP data exerts a large impact on the change in wind distributions over the sea and thus can contribute to the solution to lack of satellite and buoy data with their observational uncertainty.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.925-931
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• 2022

In this article, we compare the reliability and the hazard function between a baseline distribution and the corresponding transmuted-G distribution. Some examples based on existing transmuted-G distributions in literature are used. Three tests of parameter significance are utilized to test the importance of a transmuted-G distribution over the baseline distribution, and real data is used in an application of the inference about the importance of transmuted-G distributions.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.667-674
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• 2008

We develop new family of the t distributions for modeling semicircular data. It has convenient mathematical features. It is extended to the l-axial t distribution and a generalized semicircular t distribution.

• Communications for Statistical Applications and Methods
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• v.28 no.1
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• pp.59-79
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• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• The Korean Journal of Applied Statistics
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• v.22 no.4
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• pp.879-891
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• 2009

We developed the projected l-axial skew-normal(LASN) family of distributions for I-axial data. The LASN family of distributions contains the semicircular skew-normal(SCSN) and the circular skew-normal(CSN) families of distributions as special cases. The LASN densities are similar to the wrapped skew-normal densities for the small values of the scale parameter. However CSN densities have more heavy tails than those of the wrapped skew-normal densities on the circle. Furthermore the CSN densities have two modes as the scale parameter increases. The LASN distribution has very convenient mathematical features. We extend the LASN family of distributions to a bivariate case.

• Communications for Statistical Applications and Methods
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• v.27 no.4
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• pp.397-412
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• 2020

In this paper, a notion of data depth is used to propose nonparametric multivariate two sample tests for difference between scale parameters. Data depth can be used to measure the centrality or outlying-ness of the multivariate data point relative to data cloud. A difference in the scale parameters indicates the difference in the depth values of a multivariate data point. By observing this fact on a depth vs depth plot (DD-plot), we propose nonparametric multivariate two sample tests for scale parameters of multivariate distributions. The p-values of these proposed tests are obtained by using Fisher's permutation approach. The power performance of these proposed tests has been reported for few symmetric and skewed multivariate distributions with the existing tests. Illustration with real-life data is also provided.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.421-433
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• 2017

The CTE (conditional tail expectation) is a useful risk management measure for a diversified investment portfolio that can be generally estimated by using a transformed univariate distribution. Hong et al. (2016) proposed a multivariate CTE based on multivariate quantile vectors, and explored its characteristics for multivariate normal distributions. Since most real financial data is not distributed symmetrically, it is problematic to apply the CTE to normal distributions. In order to obtain a multivariate CTE for various kinds of joint distributions, distribution fitting methods using copula functions are proposed in this work. Among the many copula functions, the Clayton, Frank, and Gumbel functions are considered, and the multivariate CTEs are obtained by using their generator functions and parameters. These CTEs are compared with CTEs obtained using other distribution functions. The characteristics of the multivariate CTEs are discussed, as are the properties of the distribution functions and their corresponding accuracy. Finally, conclusions are derived and presented with illustrative examples.

• Journal of the Korean Data and Information Science Society
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• v.21 no.1
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• pp.195-200
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• 2010

In this paper, we consider estimators and a condence interval for a reliability in two independent right truncated Rayleigh distributions and consider the density of a ratio in two independent right truncated Rayleigh distributions. And we obtain the density of an estimator for a changing point in the density of a ratio in two independent right truncated Rayleigh distributions.