• Journal of applied mathematics & informatics
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• v.4 no.2
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• pp.469-476
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• 1997

In this paper we present a random number generation method which is one of the rejection methods, To accelerate ratio-of-uniform method we use an efficiency variable γ. After finding the optimal value of γwith respect to interesting distribution with pro-portional density random numbers can be generated in acceleration.

• Journal of the Korean Institute of Telematics and Electronics C
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• v.35C no.5
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• pp.11-16
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• 1998

We analyze the software reliability growth models for the specified period from the viewpoint of theory of differential equations. we defien a genralized form of reliability growth models as follws: dN(t)/dt = b(t)f(N(t)), Where N(t) is the number of remaining faults and b(t) is the failure rate per software fault at time t. We show that the well-known three software reliability growth models - Goel - Okumoto, s-shaped, and Musa-Okumoto model- are special cases of the generalized form. We, also, extend the generalized form into an extended form being dN(t)/dt = b(t, .gamma.)f(N(t)), The genneralized form can be obtained if the distribution of failures is given. The extended form can be used to describe a software reliabilit growth model having weibull density function as a fault exposure rate. As an application of the generalized form, we classify three mentioned models according to the forms of b(t) and f(N(t)). Also, we present a case study applying the generalized form.

• 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.

• Journal of The Korean Society of Agricultural Engineers
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• v.51 no.3
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• pp.53-62
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• 2009

This study was carried out to select optimal probability distribution based on design accumulated monthly mean inflow from the viewpoint of drought by Gamma (GAM), Generalized extreme value (GEV), Generalized logistic (GLO), Generalized normal (GNO), Generalized pareto (GPA), Gumbel (GUM), Normal (NOR), Pearson type 3 (PT3), Wakeby (WAK) and Kappa (KAP) distributions for the observed accumulative monthly mean inflow of Chungjudam. L-moment ratio was calculated using observed accumulative monthly mean inflow. Parameters of 10 probability distributions were estimated by the method of L-moments with the observed accumulated monthly mean inflow. Design accumulated monthly mean inflows obtained by the method of L-moments using different methods for plotting positions formulas in the 10 probability distributions were compared by relative mean error (RME) and relative absolute error (RAE) respectively. It has shown that the design accumulative monthly mean inflow derived by the method of L-moments using Weibull plotting position formula in WAK and KAP distributions were much closer to those of the observed accumulative monthly mean inflow in comparison with those obtained by the method of L-moment with the different formulas for plotting positions in other distributions from the viewpoint of RME and RAE.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.537-537
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• 2015

In recent decades, the independence and identical distribution (iid) assumption for extreme events has been shown to be invalid in many cases because long-term climate variability resulting from phenomena such as the Pacific decadal variability and El Nino-Southern Oscillation may induce varying meteorological systems such as persistent wet years and dry years. Therefore, in the current study we propose a new parameter estimation method for probability distribution models to more accurately predict the magnitude of future extreme events when the iid assumption of probability distributions for large-scale climate variability is not adequate. The proposed parameter estimation is based on a metaheuristic approach and is derived from the objective function of the rth power probability-weighted sum of observations in increasing order. The combination of two distributions, gamma and generalized extreme value (GEV), was fitted to the GEV distribution in a simulation study. In addition, a case study examining the annual hourly maximum precipitation of all stations in South Korea was performed to evaluate the performance of the proposed approach. The results of the simulation study and case study indicate that the proposed metaheuristic parameter estimation method is an effective alternative for accurately selecting the rth power when the iid assumption of extreme hydrometeorological events is not valid for large-scale climate variability. The maximum likelihood estimate is more accurate with a low mixing probability, and the probability-weighted moment method is a moderately effective option.

• Journal of the Korea Society of Computer and Information
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• v.27 no.8
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• pp.143-149
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• 2022

Since patent documents contain detailed results of research and development technologies, many studies on various patent analysis methods for effective technology analysis have been conducted. In particular, research on quantitative patent analysis by statistics and machine learning algorithms has been actively conducted recently. The most used patent data in quantitative patent analysis is technology keywords. Most of the existing methods for analyzing the keyword data were models based on the Gaussian probability distribution with random variable on real space from negative infinity to positive infinity. In this paper, we propose a model using gamma probability distribution to analyze the frequency data of patent keywords that can theoretically have values from zero to positive infinity. In addition, in order to determine the regression equation of the gamma-based regression model, two-mode network is constructed to visualize the technological association between keywords. Practical patent data is collected and analyzed for performance evaluation between the proposed method and the existing Gaussian-based analysis models.

• Journal of The Korean Society of Agricultural Engineers
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• v.46 no.4
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• pp.25-36
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• 2004

This study was conducted to derive the design rainfall by the consecutive duration using the at-site frequency analysis. Using the errors, K-S tests and LH-moment ratios, Log Pearson type 3 (LP3) and Generalized Extreme Value (GEV) distributions of Gamma and Non-Gamma Family, respectively were identified as the optimal probability distributions among applied distributions. Parameters of GEV and LP3 distributions were estimated by the method of L and LH-moments and the Indirect method of moments respectively. Design rainfalls following the consecutive duration were derived by at-site frequency analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE) and relative efficiency (RE) in RRMSE for the design rainfall derived by at-site analysis in the observed and simulated data were computed and compared. It has shown that at-site frequency analysis by GEV distribution using L-moments is confirmed as more reliable than that of GEV and LP3 distributions using LH-moments and Indirect method of moments in view of relative efficiency.

• Nuclear Engineering and Technology
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• v.7 no.4
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• pp.285-293
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• 1975

A result of the study to determine the depth-dose distribution along the central axis of a polyethylene sphere in diameter of 30cm is described. Depth-dose distribution in the polyethylene sphere for broad beam of monoenergetic photons has been experimentally determined with thermoluminescent dosimeter as a cavity dosimeter. The conversion of dose absorbed in the LiF TLD to dose in the surrounding medium was carried out on the basis of Burlin's generalized cavity theory. Presented in graphical forms are the results obtained. The maximum absorbed doses in the sphere were observed at the depth of about 0.3cm and 0.5cm from the surface of the sphere for the gamma-rays of $^{137}$ Cs and $^{60}$ Co, respectively.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.533-540
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• 1997

일반화 감마분포(generalized gamma distribution)에서 지표모수(index parameter)에 대한 추론은 생존시간(lifetime)과 관련한 모형의 선택문제에서 매우 중요하다. 이에 대한 정확한(exact) 추론법은 알려져 있지 않다. 본 연구에서는 이에 대한 점근적(asymptotic) 검정법으로 소표본에서도 우도비 검정에 비해 효율이 뛰어난 Bartlett 검정을 제안하고, 이의 요율적 수행을 위한 대체 모형으로 부터의 누율계산(cumulant computation) 법을 제시하였다. 또한 실제자료에 대해 본 논문에서 제시한 누율계산과정을 이용하여 Bartlett 검정을 실시한 결과 기존의 우도비 검정과는 상당히 큰 차이가 남을 확인하였다. 따라서 모형의 선택 등의 문제에서 제안된 방법은 소표본의 경우에 더욱 효율적이라 할 수 있다.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.501-510
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• 2008

The distribution of the sum of n independent random variables having exponential distributions with different parameters ${\beta}_i$ ($i=1,2,{\ldots},n$) is given in [2], [3], [4] and [6]. In [1], by using Laplace transform, Jasiulewicz and Kordecki generalized the results obtained by Sen and Balakrishnan in [6] and established a formula for the distribution of this sum without conditions on the parameters ${\beta}_i$. The aim of this note is to present a method to find the distribution of the sum of n independent exponentially distributed random variables with different parameters. Our method can also be used to handle the case when all ${\beta}_i$ are the same.