• The Korean Journal of Applied Statistics
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• v.27 no.5
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• pp.819-831
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• 2014

The Exact-EM algorithm can conventionally fit a mixture of multivariate skew distribution. However, it suffers from highly expensive computational costs to calculate the moments of multivariate truncated t-distribution in E-step. This paper proposes a new SPU-EM method that adopts the AECM algorithm principle proposed by Meng and van Dyk (1997)'s to circumvent the multi-dimensionality of the moments. This method offers a shorter execution time than a conventional Exact-EM algorithm. Some experments are provided to show its effectiveness.

• Communications for Statistical Applications and Methods
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• v.21 no.5
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• pp.461-469
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• 2014

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

• Communications for Statistical Applications and Methods
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• v.19 no.5
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• pp.673-683
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• 2012

Cabral et al. (2012) defined a mixture model of multivariate skew t-distributions(STMM), and proposed the use of an ECME algorithm (a variation of a standard EM algorithm) to fit the model. Their estimation by the ECME algorithm is closely related to the estimation of the degree of freedoms in the STMM. With the ECME, their purpose is to escape from the calculation of a conditional expectation that is not provided by a closed form; however, their estimates are quite unstable during the procedure of the ECME algorithm. In this paper, we provide a conditional expectation as a closed form so that it can be easily calculated; in addition, we propose to use the ECM algorithm in order to stably fit the STMM.

• The Korean Journal of Applied Statistics
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• v.30 no.3
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• pp.363-376
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• 2017

The insurance market is saturated and its growth engine is exhausted; consequently, the insurance industry is now in a low growth period with insurance companies that face a fierce competitive environment. In such a situation, it will be an important issue to find the probability distributions that can explain the flow of insurance claims, which are the basis of the actuarial calculation of the insurance product. Insurance claims are generally known to be well fitted by lognormal distributions or Pareto distributions biased to the left with a thick tail. In recent years, skew normal distributions or skew t distributions have been considered reasonable distributions for describing insurance claims. Cooray and Ananda (2005) proposed a composite lognormal-Pareto distribution that has the advantages of both lognormal and Pareto distributions and they also showed the composite distribution has a higher fitness than single distributions. In this paper, we introduce new composite distributions based on skew normal distributions or skew t distributions and apply them to Danish fire insurance claim data and US indemnity loss data to compare their performance with the other composite distributions and single distributions.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.129-142
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• 2024

In various industries, especially manufacturing and chemical industries, it is often observed that the distribution of a specific process, initially having followed a normal distribution, becomes skewed as a result of unexpected causes. That is, a process deviates from a normal distribution and becomes a skewed distribution. The skew-normal (SN) distribution is one of the most employed models to characterize such processes. The shape of this distribution is determined by the asymmetry parameter. When this parameter is set to zero, the distribution is equal to the normal distribution. Moreover, when there is a shift in the asymmetry parameter, the mean and variance of a SN distribution shift accordingly. In this paper, we propose procedures for monitoring the asymmetry parameter, based on the statistic derived from the noncentral t-distribution. After applying the statistic to Shewhart and the exponentially weighted moving average (EWMA) charts, we evaluate the performance of the proposed procedures and compare it with previously studied procedures based on other skewness statistics.

• Communications for Statistical Applications and Methods
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• v.27 no.2
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• pp.255-268
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• 2020

A mixture of multivariate canonical fundamental skew t-distribution (CFUST) has been of interest in various fields. In particular, interest in the unsupervised learning society is noteworthy. However, fitting the model via EM algorithm suffers from significant processing time. The main cause is due to the calculation of many multivariate t-cdfs (cumulative distribution functions) in E-step. In this article, we provide an approximate, but fast calculation method for the in univariate fashion, which is the product of successively conditional univariate t-cdfs with Taylor's first order approximation. By replacing all multivariate t-cdfs in E-step with the proposed approximate versions, we obtain the admissible results of fitting the model, where it gives 85% reduction time for the 5 dimensional skewness case of the Australian Institution Sport data set. For this approach, discussions about rough properties, advantages and limits are also presented.

• The Korean Journal of Applied Statistics
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• v.16 no.1
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• pp.101-115
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• 2003

Lately there has been much theoretical and applied interest in linear models with non-normal heavy tailed error distributions. Starting Zellner(1976)'s study, many authors have explored the consequences of non-normality and heavy-tailed error distributions. We consider hierarchical models including selection models under a skewed heavy-tailed e..o. distribution proposed originally by Chen, Dey and Shao(1999) and Branco and Dey(2001) with Dirichlet process prior(Ferguson, 1973) in order to use a meta-analysis. A general calss of skewed elliptical distribution is reviewed and developed. Also, we consider the detail computational scheme under skew normal and skew t distribution using MCMC method. Finally, we introduce one example from Johnson(1993)'s real data and apply our proposed methodology.

• Journal of the Korean Statistical Society
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• v.35 no.4
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• pp.419-439
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• 2006

The article develops a new class of distributions by introducing a nonnegative perturbing function to $t_\nu$ distribution having location and scale parameters. The class is obtained by using transformations and conditioning. The class strictly includes $t_\nu$ and $skew-t_\nu$ distributions. It provides yet other models useful for selection modeling and robustness analysis. Analytic forms of the densities are obtained and distributional properties are studied. These developments are followed by an easy method for estimating the distribution by using Markov chain Monte Carlo. It is shown that the method is straightforward to specify distribution ally and to implement computationally, with output readily adopted for constructing required criterion. The method is illustrated by using a simulation study.

• Proceedings of the KIEE Conference
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• 1995.07c
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• pp.1187-1189
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• 1995

The paper is concerned with the pre-arcing behavior of rapid current limiting fuselink using copper as a melting element. The phenomenon is faced by a numerical simulation(especially, FDM is applicated) of the melting element. Through the results, we can know the trends of the I-t characteristics and temperature distribution along the x axis for different fuselink shapes with circular, rectangular, and skew restriction type respectively, to be good for designing the optimal element.

• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.139-169
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• 2009

This paper introduces the modified VaR which takes into account the asymmetry and fat-tails of financial asset distribution, and then compares its out-of-sample forecast performance with traditional VaR model such as historical simulation model and Riskmetrics. The empirical tests using stock indices of 6 countries showed that the modified VaR has the best forecast accuracy. At the test of independence, Riskmetrics and GARCH model showed best performances, but the independence was not rejected for the modified VaR. The Monte Carlo simulation using skew t distribution again proved the best forecast performance of the modified VaR. One of many advantages of the modified VaR is that it is appropriate for measuring VaR of the portfolio, because it can reflect not only the linear relationship but also the nonlinear relationship between individual assets of the portfolio through coskewness and cokurtosis. The empirical analysis about decomposing VaR of the portfolio of 6 stock indices confirmed that the component VaR is very useful for the re-allocation of component assets to achieve higher Sharpe ratio and the active risk management.