• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.357-365
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• 2007

In this paper we present characterizations of the Pareto, Lomax, exponential and beta models by some properties of their $r^{th}$ partial moment defined as ${\alpha}_r(t)=E[(X-t)^+]^r$, where $(X-t)^+ = max(X-t,0)$. Given the partial moments at a few truncation points, these results enable us to calculate the moments at many other points.

• Bulletin of the Korean Chemical Society
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• v.16 no.10
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• pp.915-923
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• 1995

The parameters for an empirical net atomic charge calculation method, Modified Partial Equalization of Orbital Electronegativity (MPEOE), were determined for the atoms in organosilicon compounds and zeolites. For the organosilicon family, the empirical parameters were determined by introducing both experimental and ab initio observables as constraints, these are the experimental and ab initio dipole moments, and the ab initio electrostatic potential of the organosilicon molecules. The Mulliken population was also introduced though it is not a quantum mechanical observable. For the parameter optimization of the atoms in the aluminosilicates, the dipole moments and the electrostatic potentials which calculated from the 6-31G** ab initio wave function were used as constraints. The empirically calculated atomic charges of the organosilicons could reproduce both the experimental and the ab inito dipole moments well. The empirical atomic charges of the aluminosilicates could reproduce the ab initio electrostatic potentials well also.

• Journal of Integrative Natural Science
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• v.3 no.4
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• pp.231-236
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• 2010

Partial charge is an important and fundamental concept which can explain many aspects of chemistry. Since a molecule can be regarded as neclei surrounded by electron cloud, there is no way to define a partial charge accurately. Nevertheless, there have been many attempts to define these seemingly impossible parameters, since they would facilitate the understanding of molecular properties such as molecular dipole moment, solvation, hydrogen bonding, molecular spectroscopy, chemical reaction, etc. Common methods are based on the charge equalization, orbital occupancy, charge density, and electric multipole moments, and electrostatic potential fitting. Methods based on the charge equalization using electronegativity are very fast, and therefore they have been used to study many compounds. Methods to subdivide orbital occupancy using basis set conversion, relies on the notion that molecular orbitals are composed of atomic orbitals. The main idea is to reduce overlap integral between two nuclei using converted orthogonal basis sets. Using some quantum mechanical observables like electrostatic potential or charge multipole moments. Using potential grids obtained from wavefunction, partial charges can be fitted. these charges are most useful to describe intermolecular electrostatic interactions. Methods to using dipole moment and its derivatives, seems to be sensitive the level of theory, Dividing electron density using density gradient being the most rigorous theoretically among various schemes, bears best potential to describe the charge the most adequately in the future.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.3
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• pp.45-55
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• 2000

This study was carried out to derive optimal design low flows bythe Weibull-3 and Wakeby distributions for the partial consecutive duration series at seven watersheds along Han. nagdong, Geum Yeongsan and Seomjin river systems. L-coefficient of variation L-skewness and L-kurtosis were calculated by the L-moment ratio respectively. Parameters were estimated by the method of L-Moments with consecutive duration. Design low flows obtained by method of L-Moments using with consecutive duration, Design low flows obtained by method of L-Moments using different methods for plotting positions formulas in the Weibull-3 and Wakeby distributions were compared by the Root Mean Square Errors(RMSE). It has shown that design low flows derived by the method of L-moments using Weivull plotting position formula in Wakeby distribution were much closer to those of the observed data in comparison with those obtained by the methods of L-moments with the different formulas for plotting positions in Weibull-3 distribution from the viewpoint of Root Mean Square Errors.

• Journal of the Korean Operations Research and Management Science Society
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• v.31 no.1
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• pp.83-90
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• 2006

By defining the partial busy period of the M/M/c/K queueing system as the time interval during which at least one server is in service, we derive the first two moments of both the partial busy period and the number of customers served during it. All expressions are given in explicit forms.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.157-160
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• 1999

We show the cumulants of a minimal sufficient statistics in k parameter natural exponential family by parameter function and partial parameter function. We nd the cumulants have some merits of central moments and general cumulants both. The first three cumulants are the central moments themselves and the fourth cumulant has the form related with kurtosis.

• Communications for Statistical Applications and Methods
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• v.8 no.2
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• pp.311-317
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• 2001

It is necessary to check the linearity of selected covariates in regression diagnostics. There are various graphical methods using residual plots such as partial residual plots, augmented partial residual plots and combining conditional expectation and residual plots. In this paper, we propose the modified pseudolikelihood ratio test statistics based on these residual plots to test linearity of selected covariate. These test statistics which measure the distance between the nonparametric and parametric models are derived as a ratio of quadratic forms. The approximate distribution of these statistics is calculated numerically by using three moments. The power comparison of these statistics is given.

• Journal of Environmental Science International
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• v.8 no.4
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• pp.431-441
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• 1999

In this study, the regional frequency analysis is used to determine each subbasin drought frequency with reliable monthly precipitation and the L-Moments method which is almost unbiased and has very nearly a normal distribution is used for the parameter estimation of monthly precipitation time series in Nakdong river basin. As the result of this study, the duration of '93-'94 is most severe drought year than any other water year and the drought frequency is established as compared the regional frequency analysis result of cumulative precipitation of 12th duration months in each subbasin with that of 12th duration months in the major drought duration. The Linear regression equation is induced according to linear regression analysis of drought frequency between Nakdong total basin and each subbasin of the same drought duration. Therefore, as the foundation of this study, it can be applied proposed method and procedure of this study to the water budget analysis considering safety standards for the design of impounding facilities large-scale river basin and for this purpose, above all, it is considered that expansion of reliable preciptation data is needed in watershed rainfall station.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.37-41
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• 1995

In order to analyze the rolling motion of a ship in random beam waves we use the partial stochastic linearization method. The quadratic damping and the nonlinear restoring moments given by the odd polynomials up to the 11th order are added to a single degree of freedom linear equation of roll motion. The irregular excitation moment is assumed to be the Gaussian white noise. The statistical characteristics of the response by the partial stochastic linearization method is compared with results by the equivalent linearization method and Monte Carlo simulation. It is fecund that the partial stochastic linearization method is not necessarily superior to the equivalent linearization method.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.2
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• pp.78-85
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• 2000

The moment equations of the concentration distribution for the multi-region model are derived using the method of moment. The method originally devised by Aris is to obtain the concentration moments satisfying a given PDE (Partial Differential Equation. The method of moment is used to obtain the first five moments (0th to 4to) that satisfy the model PDE. Each moment of the concentration distribution for the model equation is plotted for the dimensionless time and gave similar results except the skewness and the kurtosis. The results of the analysis show the physical meaning of each moment. The comparisons with the number of regions or the global interaction coefficient give a possibility to determine the parameters of the multi-region model with the analytical concepts.