• Communications for Statistical Applications and Methods
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• v.28 no.4
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• pp.393-410
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• 2021

The Korean Long-Term Care Insurance (K-LTCI) provides financial support for long-term care service to people who need various types of assistance with daily activities. As the number of elderly people in Korea is expected to increase in the future, the demand for long-term care insurance would also increase over time. Projection of future expenditure on K-LTCI depends on the number of beneficiaries within the grading system of K-LTCI based on the test scores of applicants. This study investigated the suitability of mixture distributions to the model K-LTCI score distribution using recent empirical data on K-LTCI, provided by the National Health Insurance Service (NHIS). Based on the developed mixture models, the number of beneficiaries in each grade and its variability under the current grading system were estimated by simulation. It was observed that a mixture model is suitable for K-LTCI score distribution and may prove useful in devising a funding plan for K-LTCI benefit payment and investigating the effects of any possible revision in the K-LTCI grading system.

• Journal of Energy Engineering
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• v.10 no.3
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• pp.183-187
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• 2001

Impedance imaging for binary mixture is a kind of nonlinear inverse problem, which is usually solved iteratively by the Newton-Raphson method. Then, the ill-posedness of Hessian matrix often requires the use of a regularization method to stabilize the solution. In this study, the Levenberg-Marquredt regularization method is introduced for the binary-mixture system with various resistivity contrasts (1:2∼1:1000). Several mixture distribution are tested and the results show that the Newton-Raphson iteration combined with the Levenberg-Marquardt regularization can reconstruct reasonably good images.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• The Korean Journal of Applied Statistics
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• v.29 no.3
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• pp.513-523
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• 2016

Fitting a mixture of multivariate skew normal distribution (MSNMix) with multiple skewness parameter vectors via EM algorithm often requires a highly expensive computational cost to calculate the moments and probabilities of multivariate truncated normal distribution in E-step. Subsequently, it is common to fit an asymmetric data set with MSNMix with a simple skewness parameter vector since it allows us to compute them in E-step in an univariate manner that guarantees a cheap computational cost. However, the adaptation of a simple skewness parameter is unrealistic in many situations. This paper proposes an approximate estimation for the MSNMix with multiple skewness parameter vectors that also allows us to treat them in an univariate manner. We additionally provide some experiments to show its effectiveness.

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.10
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• pp.1311-1317
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• 2001

To investigate only the effects of the stratified mixture distribution on initial flame propagation and combustion characteristics, the instantaneous equivalence ratio in the spark plug gap and combustion pressure were measured simultaneously In a constant volume chamber, To induce the stratified propane-air mixture distribution near the spark plug, counter-flow typed mixture injection system was used under the constant mean equivalence ratio $\Phi$$\_$mean/= 1.0 The instantaneous equivalence ratio was measured by a single-shot Raman scattering with narrow-band KrF excimer laser. The measuring error was within the limit of $\pm$ 3.5% provided that the proposed method was applied to the measured Raman signals. Judging from mass fraction burned derived from the measured pressure, the optimum combustion characteristics were shown under the condition that the local equivalence ratio in the spark plug was near 1.28$\pm$0.04, and these characteristics were more remarkable at the initial stage of combustion.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.4
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• pp.249-256
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• 1993

Numerical method is applied to predict the time variation behavior of flammable mixture formation in a two dimensional enclosure from the beginning of gas leak. Additionally experimental method is used to consider qualitative aspects. Characteristics of flammable mixture formation such as distribution of flow and fuel mass fraction at various locations in the enclosure are determined for the following parameters: the various locations of leak at the bottom and aspect ratio of the enclosure. In the case of gas leak with small leak velocity from the bottom of enclosure gravitational force affects the formation of flammable mixture. Aspect ratio of the enclosure also affects the formation of flammable mixture. The volume of the region of recirculating flow is dominant factor affecting the formation mixture.

• 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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.164-169
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• 1986

Walsh analysis is applied to the numerical specification of the volume distribution which is the key parameter in the formulation of the constitutive equations of heterogeneous media, indicating the geometrical state of the mixture. An example of two-dimensional volume distribution, its approximation, and the Walsh correlation coefficients are presented and the change of the information distribution in the operations is investigated. The phenomena of information concentration upon the large-scale Walsh coefficients are applied to the volumetric response of porous slids, clarifying the validity of the spherical-model calculation.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.803-811
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• 2012

For credit evaluation models, we extend the study of discriminatory power based on AUC obtained from a ROC curve when the number of defaults is small and distribution functions of the defaults and non-defaults are normal distributions. Since distribution functions do not satisfy normality in real world, the distribution functions of the defaults and non-defaults are assumed as normal mixture distributions based on results that the normal mixture could be better fitted than other distribution estimation methods for non-normal data. By using several AUC statistics, the discriminatory power under such a circumstance is explored and compared with those of normal distributions.