• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.289-298
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• 1998

We investigate the distribution of likelihood ratio test(LRT) of null hypothesis a sample is from single gamma with unknown shape and scale against the alternative hypothesis a sample is from a mixture of two gammas, each with unknown scale and unknown (but equal) scale. To obtain stable maximum likelihood estimates(MLE) of a mixture of two gamma distributions, the EM(Dempster, Laird, and Robin(1977))and Modified Newton(Jensen and Johansen(1991)) algorithms were implemented. Based on EM, we made a simple structure likelihood equation for each parameter and could obtain stable solution by Modified Newton Algorithms. Simulation study was conducted to investigate the distribution of LRT for sample size n = 25, 50, 75, 100, 50, 200, 300, 400, 500 with 2500 replications. To determine the small sample distribution of LRT, I considered the model of a gamma distribution with shape parameter equal to 1 + f(n) and scale parameter equal to 2. The simulation results indicate that the null distribution is essentially invariant to the value of the shape parameter. Modeling of the null distribution indicates that it is well approximated by a gamma distribution with shape parameter equal to the quantity $0.927+1.18/\sqrt{n}$ and scale parameter equal to 2.16.

• Journal of the Korean earth science society
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• v.35 no.7
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• pp.518-528
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• 2014

In this study, a model of rainfall drop-size distribution was modified using PARSIVEL-retrieved rainfall drop-size distribution over Daegwanryeong mountainous area. A prototype model (Modified ${\Gamma}$ distribution model) applicable for this area was decided through the comparative analysis between results from models proposed by preceding research and PARSIVEL-retrieved data over Daegwanryeong mountainous area. In order to apply the prototype model for Daegwanryeong region, the parameters (${\alpha}$, A, B) were made via sensitivity experiments and models of the rainfall drop-size distributions for five cases of rainfall rate were proposed. Results from the proposed five models showed high correlations with PARSIVEL-retrieved data ($R^2=0.975$). In order to suggest a generalized form of rainfall drop-size distribution, interaction equations between rainfall rates and parameters (${\alpha}$, A, B) were investigated. The generalized model of the rainfall drop-size distribution was highly correlated with PARSIVEL-retrieved data ($R^2=0.953$), which means that the proposed model from this study was effective for simulating the rainfall drop-size distribution over Daegwanryeong region. However, the proposed model was optimized for rainfall drop-size distribution over Daegwanryeong region. Therefore, broad observations of other regions are necessary in order to develop the representative model of the Korean peninsula.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.44 no.3
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• pp.303-314
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• 2024

Precipitation data are an integral part of water management planning, especially the design of hydroelectric structures and the study of floods and droughts. However, it is difficult to obtain accurate data due to space-time constraints. The recent increase in hydrological variability due to climate change has further emphasized the importance of precipitation simulation techniques. Therefore, in this study, the Modified Bartlett-Lewis Rectangular Pulse model was utilized to apply the parameters necessary to predict daily precipitation. The effect of this parameter on the daily precipitation prediction was analyzed by applying exponential distribution, Gamma distribution, and Weibull distribution to evaluate the suitability of daily precipitation prediction according to each distribution type. As a result, it is judged that parameters should be selected in consideration of regional and seasonal characteristics when simulating precipitation using the MBLRP model.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.473-495
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• 2019

In this paper, a new extension of Lindley distribution has been introduced. Certain characterizations based on truncated moments, hazard and reverse hazard function, conditional expectation of the proposed distribution are presented. Besides, these characterizations, other statistical/mathematical properties of the proposed model are also discussed. The estimation of the parameters is performed through different classical methods of estimation. Bayes estimation is computed under gamma informative prior under the squared error loss function. The performances of all estimation methods are studied via Monte Carlo simulations in mean square error sense. The potential of the proposed model is analyzed through two data sets. A modified goodness-of-fit test using the Nikulin-Rao-Robson statistic test is investigated via two examples and is observed that the new extension might be used as an alternative lifetime model.

• Nuclear Engineering and Technology
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• v.55 no.3
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• pp.1071-1083
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• 2023

The on-the-fly energy release per fission (OTFK) model is implemented in STREAM to continuously update the Kappa values during the depletion calculation. The explicit neutron and photon energy distribution, which has not been considered in previous STREAM versions, is incorporated into the existing on-the-fly model. The impacts of the modified OTFK model with explicit neutron and photon heating in STREAM on the power distribution, fuel temperature, and other core parameters during depletion with feedback calculations are studied using several problems from the VERA benchmark suit. Overall, the explicit heating calculation provides a better power map for the feedback calculations particularly when strong gamma emitters are present. Generally, the fuel temperature decreases when neutron and photon heating is employed because fission neutrons and gamma rays are transported away from their points of generation. This energy release model in STREAM indicates that gamma energy accounts for approximately 9.5%-10% of the total energy released, and approximately 2.4%-2.6% of the total energy released will be deposited in the coolant for the VERA 5, NuScale, and Yonggwang Unit 3 2D cores.

• Journal of Korea Water Resources Association
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• v.52 no.9
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• pp.603-613
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• 2019

This study proposes a method to generate runoff ensemble members using a rainfall-runoff model based on the shot noise process (hereafter the rainfall-runoff model). The proposed method was applied to generate runoff ensemble members for three drainage basins of Daerim 2, Guro 1 and the Jungdong, whose results were then compared with the observed. The parameters of the rainfall-runoff model were estimated using the empirical formulas like the Kerby, Kraven II and Russel, also the concept of modified rational formula. Gamma and exponential distributions were used to generate random numbers of the parameters of the rainfall-runoff model. Especially, the gamma distribution is found to be useful to generate various random numbers depending on the pre-assigned relationship between mean and standard deviation. Comparison between the generated runoff ensemble members and the observed shows that those runoff ensemble members generated using the gamma distribution with its standard deviation twice of the mean properly cover the observed runoff.

• Journal of the Korean Professional Engineers Association
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• v.16 no.3
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• pp.68-73
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• 1983

The metal deposition behavior in the barrel tin plating has been studied for the electronic DIP products, and tried to find out some modified factors in order to explain partial ,current flow behavior of this load. The deposition distribution characteristics for DTP products should be classified with the normal barrel plating as partially conductive load. Deposit distribution curves obtained from one-dimensional model have shown strong dependence n the applied current density, rotating speed of barrel and metal ion concentration of the solution. Theoretical formula J=$\delta$'/${\beta}$-{-c$^3$/${\gamma}$-exp-(1-${\alpha}$)n${\Phi}$} derived from one-dimensional porous model has been proposed for the barrel plating behavior where higher overpotential and concentration changes take place during barrel plating.

• Publications of The Korean Astronomical Society
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• v.30 no.2
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• pp.385-387
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• 2015

Stellar mass is an important parameter of galaxies. We estimate the dynamical mass of an elliptical galaxy by its velocity dispersion and effective radius using the Hernquist model in the framework of MOdified Newtonian Dynamics (MOND). MOND is an alternative theory to the dark matter paradigm. In MOND the dynamical mass is the same as the baryonic mass or luminous mass, and in elliptical galaxies most of the baryons reside in stars. We select elliptical galaxies between redshift 0.05 and 0.5 from the main galaxy sample and the luminous red galaxy sample in the Sloan Digital Sky Survey. We find that the stellar mass-to-light ratio at different redshift epochs can be fitted by a gamma distribution, and its mean is smaller at smaller redshifts.

• Journal of the Korean Society for Nondestructive Testing
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• v.26 no.1
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• pp.1-6
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• 2006

Using In-113m emitting gamma ray of 0.392MeV at radioisotope tracer the RTD (residence time distribution) of water in the flocculator of wastewater treatment facility was measured. The result was analyzed mathematically using K-RTD program constructed on the basis of CFSTR (constant flow stirred tank reactor) model. The mean residence time and the tank number are the main parameters which describe the flow behavior of the system. Those parameters were obtained in the fitting profess of the simulated curves to the experimental results. It was suggested to construct a modified numerical model to describe the bypass flow which was observed in the experiment.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.22 no.3
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• pp.149-155
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• 2010

The existing formula for estimating the wave overtopping are mainly about the perpendicularly incident wave to the structure and wave overtopping formula for the obliquely incident wave are rare. Moreover, these formula present only the overtopping reduction factor(${\gamma}_{\beta}$) with respect to the incident wave angle rather than the spatial distribution of overtopping along the structures because the length of model is relatively too short for the wave to propagate along the structure. In this study, the wave overtopping reduction factor considering the spatial variation of wave overtopping along the vertical wall is investigated using the hydraulic model tests and the results are compared with the those of EurOtop(2007). The wave overtopping reduction factor is modified for ${\beta}$ > $45^{\circ}$ condition.