• The Transactions of the Korean Institute of Electrical Engineers
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• v.40 no.1
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• pp.1-9
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• 1991

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charlier expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modeling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we further developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A. and Booth-Baleriaux method. It is verified that the M.O.C.A. method is faster and more accure than any other method.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.219-229
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• 2010

There have been many researches on the risk management due to rapid increase of various risk factors for financial assets. Aa a method for comprehensive risk management, Value at Risk (VaR) is developed. For estimation of VaR, it is important task to solve the problem of asymmetric distribution of the return rate with heavy tail. Most real distributions of the return rate have high positive kurtosis and low negative skewness. In this paper, some alternative distributions are used to be fitted to real distributions of the return rate of financial asset. And estimates of VaR obtained by using these fitting distributions are compared with those obtained from real distribution. It is found that normal mixture distribution is the most fitted where its skewness and kurtosis of practical distribution are close to real ones, and the VaR estimation using normal mixture distribution is more accurate than any others using other distributions including normal distribution.

• Proceedings of the KIEE Conference
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• 1990.07a
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• pp.154-157
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• 1990

This paper describes a new method of calculating expected energy generation and loss of load probability (L.O.L.P) for electric power system operation and expansion planning. The method represents an equivalent load duration curve (E.L.D.C) as a mixture of cumulants approximation (M.O.C.A), which is the general case of mixture of normals approximation (M.O.N.A). By regarding a load distribution as many normal distributions-rather than one normal distribution-and representing each of them in terms of Gram-Charller expansion, we could improve the accuracy of results. We developed an algorithm which automatically determines the number of distribution and demarcation points. In modelling of a supply system, we made subsets of generators according to the number of generator outage: since the calculation of each subset's moment needs to be processed rapidly, we futher developed specific recursive formulae. The method is applied to the test systems and the results are compared with those of cumulant, M.O.N.A and Booth-Baleriaux method. It is verified that the M.O.C.A method is faster and more accurate than any other methods.

• Journal of the Korean Statistical Society
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• v.26 no.4
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• pp.477-491
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• 1997

A new predictive classification rule for assigning future cases into one of two multivariate normal population (with unknown normal mixture model) is considered. The development involves calculation of posterior probability of each possible normal-mixture model via a default Bayesian test criterion, called intrinsic Bayes factor, and suggests predictive distribution for future cases to be classified that accounts for model uncertainty by weighting the effect of each model by its posterior probabiliy. In this paper, our interest is focused on constructing the classification rule that takes care of uncertainty about the types of covariance matrices (homogeneity/heterogeneity) involved in the model. For the constructed rule, a Monte Carlo simulation study demonstrates routine application and notes benefits over traditional predictive calssification rule by Geisser (1982).

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1397-1403
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• 2006

This paper considers the testing problem for scale changes in autoregressive processes with heavy-tailed innovations. For a test, we propose the CUSUM test statistic based on the trimmed residuals. We perform a simulation study for the mixture normal and Cauchy innovations.

• ETRI Journal
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• v.33 no.6
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• pp.949-952
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• 2011

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.8
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• pp.297-309
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• 2021

In this study, to capture the skewness and kurtosis detected in both conditional and unconditional return distributions of the stock markets of Kazakhstan and Russia, two versions of normal mixture GARCH models are employed. The data set consists of daily observations of the Kazakhstan and Russia stock prices, and world crude oil price, covering the period from 1 June 2006 through 1 March 2021. From the empirical results, incorporating the long memory effect on the returns not only provides better descriptions of dynamic behaviors of the stock market prices but also plays a significant role in improving a better understanding of the return dynamics. In addition, normal mixture models for time-varying volatility provide a better fit to the conditional densities than the usual GARCH specifications and has an important advantage that the conditional higher moments are time-varying. This implies that the volatility skews implied by normal mixture models are more likely to exhibit the features of risk and the direction of the information flow is regime-dependent. The findings of this study contain useful information for diverse purposes of cross-border stock market players such as asset allocation, portfolio management, risk management, and market regulations.

• Communications for Statistical Applications and Methods
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• v.18 no.3
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• pp.343-355
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• 2011

For a data with the assumption of the mixture distribution, it is important to find an appropriate threshold and evaluate its performance. The relationship is found of well-known nine classification accuracy measures such as MVD, Youden's index, the closest-to-(0, 1) criterion, the amended closest-to-(0, 1) criterion, SSS, symmetry point, accuracy area, TA, TR. Then some conditions of these measures are categorized into seven groups. Under the normal mixture assumption, we calculate thresholds based on these measures and obtain the corresponding type I and II errors. We could explore that which classification measure has minimum type I and II errors for estimated mixture distribution to understand the strength and weakness of these classification measures.

• The Korean Journal of Applied Statistics
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• v.25 no.4
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• pp.651-659
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• 2012

In this paper we developed a statistical model for circular data with noises. In this case, model fitting by single circular model has a lack-of-fit problem. To overcome this problem, we consider some mixture models that include circular uniform distribution and apply an EM algorithm to estimate the parameters. Both von Mises and Wrapped skew normal distributions are considered in this paper. Simulation studies are executed to assess the suggested EM algorithms. Finally, we applied the suggested method to fit 2008 EHFRS(Epidemic Hemorrhagic Fever with Renal Syndrome) data provided by the KCDC(Korea Centers for Disease Control and Prevention).

• The Korean Journal of Applied Statistics
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• v.25 no.6
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• pp.1037-1047
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• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.