• The Korean Journal of Applied Statistics
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• v.26 no.1
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• pp.141-149
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• 2013

We present methods for studying the log-density ratio that enables the selection of the predictors and the form to be included in the logistic regression model. Under bivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of two predictors. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms. We also explore other conditions in which the crossproduct and quadratic terms are not needed in the logistic regression model.

• KIEE International Transactions on Power Engineering
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• v.5A no.4
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• pp.403-411
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• 2005

At present, the Cournot model is one of the most commonly used theories to analyze the gaming situation in an oligopoly type market. However, several problems exist in the successful application of this model to the electricity market. The representative one is obtaining the inverse demand curve able to be induced from the relationship between market price and demand response. In the Cournot model, each player offers their generation quantity to obtain maximum profit, which is accomplished by reducing their quantity compared with available total capacity. As stated above, to obtain the probable Cournot equilibrium to reflect the real market situation, we have to induce the correct demand function first of all. Usually the correlation between price and demand appears over the long-term through statistical data analysis (for example, regression analysis) or by investigating consumer utility functions of several consumer groups classified as residential, industrial, and commercial. However, the elasticity has a tendency to change continuously according to the total market demand size or the level of market price. Therefore it should be updated as the trading period passes by. In this paper we propose a method for inducing and updating this price elasticity of demand function for more realistic market equilibrium.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.2
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• pp.67-78
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• 1990

An inverse self-iterative procedure is developed to determine layer moduli which are significant for the structural evaluation of pavements in developing rational and analytical rehabilitation technique. Falling weight deflectometer(FWD) is adopted as a non-destructive testing(NDT)device. The layer elastic theory is used to interpret NDT data. The theoretical deflection basins of pavement structures obtained by full factorial design are used for a parametric study on the characteristics of deflection basins and regression analyses. Regression equations to estimate layer moduli of flexible pavements are proposed through the regression analyses of theoretical deflection basins. The relationships between the rate of change of moduli and deflections are developed for the efficient iteration. An inverse self-iterative procedure to ensure the accuracy of the layer moduli is proposed. Validity and applicability of the developed procedure are verified through various numerical model tests.

• Journal of Environmental Science International
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• v.3 no.3
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• pp.263-271
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• 1994

A detachment of biofilm was investigated in an inverse fluidized bed biofilm reactor(IFRBR). The biofilm thickness, 5 and the bioparticle density, Pm were decreased by the increase of Reynolds number, Re and the decrease of biomass concentration, h. The correlations were expressed as $\delta$=6l.6+16.33$b_c$-0.004Re and Ppd=0.3+0.027$b_c$- 2.93x$l0^{-5}$ no by multiple linear regression analysis method. Specific substrate removal rate, q was derived by F/M ratio and biofilm thickness as q=0.44.+0.82F/M-5.Ix10$-4^{$\delta$}$. Specific biofilm detachment rate, bds was influenced by FIM ratio and Reynolds number as $b_{ds}$=-0.26+0.26F/M+ 2.17$\times$$10^{-4}$Re. Specific biofilm deachment rate in an IFBBR was higher than that in a FBRR(fluidized bed biofilm reactor) because of the friction between air bubble and the bioparticles.

• Journal of Educational Research in Mathematics
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• v.26 no.3
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• pp.403-420
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• 2016

Some of the critical changes in the revised 2015 Korean Mathematics curriculum were that direct proportion and inverse proportion were moved from elementary school to middle school and that supplementary content related to correlation was included. These decisions were based on comparative studies of international curriculum. Therefore in this study, we selected countries for comparison; United States, England, France, Finland, Australia, Japan, Singapore, China and Taiwan. We looked into the timing and scope for direct/inverse proportion and correlation in curricula of these countries. Along with this, we established four criteria; vertical sequence, horizontal sequence, external connection, and internal connection for an analysis framework. Then we compared and analysed the direct/inverse proportion and correlation in each curriculum. As a result, in most of these curricula, the direct/inverse proportions are introduced at middle school or are introduced at elementary school and then developed further at middle school. Most of curriculums on direct/inverse proportion and correlation match the four criteria. Correlation is introduced in high school mathematics in all counties except Finland and it is dealt in diverse context introducing related concepts, for example, correlation coefficient, regression straight line, and least square. We suggested that it is necessary to refer these international trends for the next revision of curriculum.

• The Korean Journal of Applied Statistics
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• v.30 no.2
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• pp.243-257
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• 2017

In this paper, we compare several methods to approximate option prices: Edgeworth expansion, A-type and C-type Gram-Charlier expansions, a method using normal inverse gaussian (NIG) distribution, and an asymptotic method using nonlinear regression. We used two different types of approximation. The first (called the RNM method) approximates the risk neutral probability density function of the log return of the underlying asset and computes the option price. The second (called the OPTIM method) finds the approximate option pricing formula and then estimates parameters to compute the option price. For simulation experiments, we generated underlying asset data from the Heston model and NIG model, a well-known stochastic volatility model and a well-known Levy model, respectively. We also applied the above approximating methods to the KOSPI200 call option price as a real data application. We then found that the OPTIM method shows better performance on average than the RNM method. Among the OPTIM, A-type Gram-Charlier expansion and the asymptotic method that uses nonlinear regression showed relatively better performance; in addition, among RNM, the method of using NIG distribution was relatively better than others.

• Journal of the Korean Society of Radiology
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• v.81 no.3
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• pp.632-643
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• 2020

Purpose To investigate the correlation between magnetic resonance (MR) image-based radiomics features and the genomic features of breast cancer by focusing on biomolecular intrinsic subtypes and gene expression profiles based on risk scores. Materials and Methods We used the publicly available datasets from the Cancer Genome Atlas and the Cancer Imaging Archive to extract the radiomics features of 122 breast cancers on MR images. Furthermore, PAM50 intrinsic subtypes were classified and their risk scores were determined from gene expression profiles. The relationship between radiomics features and biomolecular characteristics was analyzed. A penalized generalized regression analysis was performed to build prediction models. Results The PAM50 subtype demonstrated a statistically significant association with the maximum 2D diameter (p = 0.0189), degree of correlation (p = 0.0386), and inverse difference moment normalized (p = 0.0337). Among risk score systems, GGI and GENE70 shared 8 correlated radiomic features (p = 0.0008-0.0492) that were statistically significant. Although the maximum 2D diameter was most significantly correlated to both score systems (p = 0.0139, and p = 0.0008), the overall degree of correlation of the prediction models was weak with the highest correlation coefficient of GENE70 being 0.2171. Conclusion Maximum 2D diameter, degree of correlation, and inverse difference moment normalized demonstrated significant relationships with the PAM50 intrinsic subtypes along with gene expression profile-based risk scores such as GENE70, despite weak correlations.

• Communications for Statistical Applications and Methods
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• v.19 no.1
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• pp.1-11
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• 2012

We present methods to study the log-density ratio of the conditional densities of the predictors given the response variable in the logistic regression model. This allows us to select which predictors are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. A simulation study shows that the linear and log terms are required in general. If the conditional distributions of xjy for the two groups overlap significantly, we need both the linear and log terms; however, only the linear or log term is needed in the model if they are well separated.

• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.297-306
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• 1998

We consider a graphical method for visualizing the strictly monotonic transformation of t(y) so that the regression function E(t(y)$\mid$x) is linear in the predictor vector x. Cook and Weisberg (1994) proposed an inverse response plot which relies on the results of Li & Duan (1989) to obtain consistent estimates. Based on the recursive addition of the results from the two dimensional plots, we propose a new procedure which can be used when the consistency result is in doubt.

• Communications for Statistical Applications and Methods
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• v.15 no.3
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• pp.333-342
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• 2008

Variable selection theorem in the linear regression model is extended to the analysis of covariance model. When some of regression variables are omitted from the model, it reduces the variance of the estimators but introduces bias. Thus an appropriate balance between a biased model and one with large variances is recommended.