• The Korean Journal of Financial Management
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• v.26 no.1
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• pp.165-188
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• 2009

This paper has suggested the methodology for the frontier portfolios and the optimal portfolio under the mean-VaR framework, not assuming the normal distribution and considering the investor's preferences for the higher moments of return distributions. It suggested the grid and rank approach which did not need an assumption about return distributions to find the frontier portfolios. And the optimal portfolio was selected using the utility function that considered the 3rd and the 4th moments. For the application of the methodology, weekly returns of the developed countries index, the emerging market index and the KOSPI index were used. After the frontier portfolios of the mean-variance framework and the mean-VaR framework were selected, the optimal portfolios of each framework were compared. This application compared not only the difference of the standard deviation but also the difference of the utility level and the certainty equivalent expressed by weekly expected returns. In order to verify statistical significances about the differences between the mean-VaR and the mean-variance, this paper presented the statistics which were obtained by the historical simulation method using the bootstrapping. The results showed that an investor under the mean-VaR framework had a tendency to select the optimal portfolio which has bigger standard deviation, comparing to an investor under the mean-variance framework. In addition, the more risk averse an investor is, the bigger utility level and certainty equivalent he achieves under the mean-VaR framework. However, the difference between the two frameworks were not significant in statistical as well as economic criterion.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.3
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• pp.95-100
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• 2020

Machines and facilities are physically or chemically degenerated by continuous usage. One of the results of this degeneration is the process mean shift. The representative type of the degeneration is wear of tool or machine. According to the increasing wear level, non-conforming products cost and quality loss cost are increasing simultaneously. Therefore a periodic preventive resetting the process is necessary. The total cost consists of three items: adjustment cost (or replacement cost), non-conforming cost due to product out of upper or lower limit specification, and quality loss cost due to difference from the process target value and the product characteristic value among the conforming products. In this case, the problem of determining the adjustment period or wear limit that minimizes the total cost is called the 'process mean shift' problem. It is assumed that both specifications are set and the wear level can be observed directly. In this study, we propose a new model integrating the quality loss cost, process variance, and production volume, which has been conducted in different fields in previous studies. In particular, for the change in production volume according to the increasing in wear level, we propose a generalized production quantity function g(w). This function can be applied to most processes and we fitted the g(w) to the model. The objective equation of this model is the total cost per unit wear, and the determining variables are the wear limit and initial process setting position that minimize the objective equation.

• Communications for Statistical Applications and Methods
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• v.31 no.1
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• pp.1-35
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• 2024

The assumption of homoscedasticity is one of the most crucial assumptions for many parametric tests used in the biological sciences. The aim of this paper is to compare the empirical probability of type I error and the power of ten parametric and two non-parametric tests for homoscedasticity with simulations under different types of distributions, number of groups, number of samples per group, variance ratio and significance levels, as well as through empirical data from an agricultural experiment. According to the findings of the simulation study, when there is no violation of the assumption of normality and the groups have equal variances and equal number of samples, the Bhandary-Dai, Cochran's C, Hartley's Fmax, Levene (trimmed mean) and Bartlett tests are considered robust. The Levene (absolute and square deviations) tests show a high probability of type I error in a small number of samples, which increases as the number of groups rises. When data groups display a nonnormal distribution, researchers should utilize the Levene (trimmed mean), O'Brien and Brown-Forsythe tests. On the other hand, if the assumption of normality is not violated but diagnostic plots indicate unequal variances between groups, researchers are advised to use the Bartlett, Z-variance, Bhandary-Dai and Levene (trimmed mean) tests. Assessing the tests being considered, the test that stands out as the most well-rounded choice is the Levene's test (trimmed mean), which provides satisfactory type I error control and relatively high power. According to the findings of the study and for the scenarios considered, the two non-parametric tests are not recommended. In conclusion, it is suggested to initially check for normality and consider the number of samples per group before choosing the most appropriate test for homoscedasticity.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.40 no.1
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• pp.165-172
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• 2017

Machines are physically or chemically degenerated by continuous usage. One of the results of this degeneration is the process mean shift. Under the process mean shift, production cost, failure cost and quality loss function cost are increasing continuously. Therefore a periodic preventive resetting the process is necessary. We suppose that the wear level is observable. In this case, process mean shift problem has similar characteristics to the maintenance policy model. In the previous studies, process mean shift problem has been studied in several fields such as 'Tool wear limit', 'Canning Process' and 'Quality Loss Function' separately or partially integrated form. This paper proposes an integrated cost model which involves production cost by the material, failure cost by the nonconforming items, quality loss function cost by the deviation between the quality characteristics from the target value and resetting the process cost. We expand this process mean shift problem a little more by dealing the process variance as a function, not a constant value. We suggested a multiplier function model to the process variance according to the analysis result with practical data. We adopted two-side specification to our model. The initial process mean is generally set somewhat above the lower specification. The objective function is total integrated costs per unit wear and independent variables are wear limit and initial setting process mean. The optimum is derived from numerical analysis because the integral form of the objective function is not possible. A numerical example is presented.

• Journal of Acupuncture Research
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• v.21 no.1
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• pp.176-188
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• 2004

This study was carried out to investigate statistical validity of medical articles that used various statistical techniques such as t-test, analysis of variance, correlation analysis, regression analysis and chi-square test. For study 429 original articles using those statistical methods were selected from Journal of Korean Acupuncture & Moxibusition Society published from 1984 to 2002. 429 original articles were reviewed to analyzed the statistical procedures. Results are summarized as follows : 1. In this study 93 articles(21.68%) of 429 ones didn't report statement of statistical method in detail. 2. 53 articles(12.53%) didn't report p-value in correctly, and 245 articles(57.11 %) used mean${\pm}$standard error (Mean${\pm}$SEM.) and 109 articles used mean${\pm}$standard deviation(Mean${\pm}$SD.). All of 23 articles using nonparametric statistical techniques made an error to central tendency or dispersion. 3. 175 articles(59.93%) and 14 articles(4.79%) of 292 ones made an error to description of equal variances and normal distribution. 4. 99 articles(50%) of 185 ones misused t-test and 4 articles of 5 ones misused chi-square test. 5. 28 articles(73.68%) of 38 ones using discrete variable misused parametric technique such as t-test or ANOVA. 2 articles and 1 article of 125 ones choosing paired samples misused independent t-test and Mann-Whitney U test. 6. 20 articles using analysis of variance didn't use multiple comparison.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.575-589
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• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.

• Journal of Korean Institute of Industrial Engineers
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• v.19 no.1
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• pp.61-71
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• 1993

We focus on a way of combining the Monte Calro methods of antithetic variates and control variates to reduce the variance of the estimator of the mean response in a simulation experiment. Combined Method applies antithetic variates (partially) for driving approiate stochastic model components to reduce the vaiance of estimator and utilizes the correlations between the response and control variates. We obtain the variance of the estimator for the response analytically and compare Combined Method with control variates method. We explore the efficiency of this method in reducing the variance of the estimator through the port operations model. Combined Method shows a better performance in reducing the variance of estimator than methods of antithetic variates and control variates in the range from 6% to 8%. The marginal efficiency gain of this method is modest for the example considered. When the effective set of control variates is small, the marginal efficiency gain may increase. Though these results are from the limited experiments, Combined Method could profitably be applied to large-scale simulation models.

• Korean Journal of Food Science and Technology
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• v.26 no.1
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• pp.57-61
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• 1994

Performance of panelists trained for cooked rice quality was evaluated using analysis of variance, correlation analysis, and principal component analysis. Each method offered different information. Results showed that panleists with high F ratios (p=0.05) did not always have high correlation coefficient (p=0.05) with mean values pooled from whole panel. The results of analysis of variance for the panelists whose performance were extremely good or extremely poor were consistent with those of correlation analysis. Outliers designated by principal component analysis were different from the panelists whose performance was defined as extremely good or extremely poor by analysis of variance and correlation analysis. The results of principal component analysis descriminated the panelists with different scoring range more than different scoring trends depending on the treatments. Our study suggested combination of analysis of variance and correlation analysis provided valid basis for screening panelists.

• Journal of Information Processing Systems
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• v.16 no.4
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• pp.832-844
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• 2020

The degree of dispersion of a random variable can be described by the variance, which reflects the distance of the random variable from its mean. However, the time complexity of the traditional variance calculation algorithm is O(n), which results from full calculation of all samples. When the number of samples increases or on the occasion of high speed signal processing, algorithms with O(n) time complexity will cost huge amount of time and that may results in performance degradation of the whole system. A novel multi-step recursive algorithm for variance calculation of the time-varying data series with O(1) time complexity (constant time) is proposed in this paper. Numerical simulation and experiments of the algorithm is presented and the results demonstrate that the proposed multi-step recursive algorithm can effectively decrease computing time and hence significantly improve the variance calculation efficiency for time-varying data, which demonstrates the potential value for time-consumption data analysis or high speed signal processing.

• Atmosphere
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• v.18 no.4
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• pp.475-483
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• 2008

The hourly precipitation data from 1973 to 2007 observed at 60 weather stations over Korea are used to characterize the diurnal and semidiurnal cycles of total precipitation amount, intensity and frequency and examine their spatial patterns and interannual variations. The results show that the diurnal cycle peaks in the morning (03-09LST) and the semidiurnal cycle peaks in the late afternoon (16-20LST). It is found that the spatial variations of the peak phase of diurnal or semidiurnal cycle relative to their corresponding seasonal mean cycle are considerably small (large) for total precipitation amount and intensity (frequency, respectively) in both winter and summer seasons. Also, the diurnal phase variations for individual years relative to the seasonal mean precipitation show the significant interannual variability with dominant periods of 2-5 years for all three elements of precipitation and the slightly decreasing trend in total precipitation amount and intensity. To compare the relative contributions of frequency and intensity to the diurnal and semidiurnal cycles (and their sum) of total precipitation amount, the percentage variance of each cycle of precipitation amount explained by frequency is estimated. The fractional variance accounted for by precipitation intensity is greater than that of frequency for these three cycles. All above analyses suggest that intensity plays a more important role than frequency in the diurnal variations of total precipitation amount.