• Journal of the Korean Society of Marine Environment & Safety
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• v.21 no.3
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• pp.253-258
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• 2015

The purpose of this study is to find suitable probability distribution function of complex distribution data like multimodal. Normal distribution is broadly used to assume probability distribution function. However, complex distribution data like multimodal are very hard to be estimated by using normal distribution function only, and there might be errors when other distribution functions including normal distribution function are used. In this study, we experimented to find fit probability distribution function in multimodal area, by using AIS(Automatic Identification System) observation data gathered in Mokpo port for a year of 2013. By using chi-squared statistic, gaussian mixture model(GMM) is the fittest model rather than other distribution functions, such as extreme value, generalized extreme value, logistic, and normal distribution. GMM was found to the fit model regard to multimodal data of maritime traffic flow distribution. Probability density function for collision probability and traffic flow distribution will be calculated much precisely in the future.

• Water for future
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• v.7 no.2
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• pp.107-111
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• 1974

Annual runoff in the Nakdong river basin has been analyzed to find the probability functions of best fit to distribution of historical annual runoff. The results obtained are as follows; (1) Log-normal 3-parameter disrtibution is believed as the probability function of best fit to historical distribution (2) Log-normal 3-parameter disrtibution is believed as the best fit probability function among Log-normal dist-ributions. (3) In the test of goodness of fit, $x^2-test$ shows that probability of $x^2-valus$ in Log-normal 3-parameter distribution is nearly more than 90%. But in the Simirnov-Kolmogorov test, hypotheses for the probability distributions cannot be rejected at significance level 5% & 1%. (4) Among 7 gauging stations, Dongchon & Koryung-Bridge's records show lower fitness to the theoretical probability functions than other 5 gauging station's

• ETRI Journal
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• v.32 no.6
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• pp.965-968
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• 2010

In this letter, we derive the distribution functions of five ratios involving two correlated Gaussian random variables by using the rotation of Cartesian coordinates. The results can be used in evaluating the various probability performances of wireless communications systems.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.30 no.5A
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• pp.425-431
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• 2010

The phase distribution in a multi-phase material strongly affects its material properties. Therefore, a proper method to describe the phase distribution of a material is needed. In this research, probability distribution functions, two-point correlation and lineal-path functions, are used to represent the probabilistic phase distributions of a material. The probability distribution function is calculated using a numerical method and is described as an analytical form via exponential curve fitting with three parameters. Application of analytical form of probability distribution function is investigated using two-phase polycrystalline solids and soil samples. It is confirmed that the probability distribution functions can be represented as an exponential form using curve fitting which helps identifying the applicability of a representative volume element(RVE).

• Proceedings of the Korean Society of Agricultural Engineers Conference
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• 1998.10a
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• pp.338-343
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• 1998

This study is to select appropriate probability distributions for ten days evaporation data for the purpose of representing statistical characteristics of real evaporation data in Korea. Nine probability distribution functions were assumed to be underlying distributions for ten days evaporation data of 20 stations with the duration of 20 years. The parameter of each probability distribution function were estimated by the maximum likelihood approach, and appropriate probability distributions were selected from the goodness of fit test. Log Pearson type III model was selected as an appropriate probability distribution for ten days evaporation data in Korea.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.408-413
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• 2005

A new methodology for discrete non-Gaussian probability density estimation is investigated in this paper based on a dynamic Bayesian network (DBN) and kernel functions. The estimator consists of a DBN in which the transition distribution is represented with kernel functions. The estimator parameters are determined through a recursive learning algorithm according to the maximum likelihood (ML) scheme. A discrete-type Poisson distribution is generated in a simulation experiment to evaluate the proposed method. In addition, an unknown probability density generated by nonlinear transformation of a Poisson random variable is simulated. Computer simulations numerically demonstrate that the method successfully estimates the unknown probability distribution function (PDF).

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1A
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• pp.31-37
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• 2012

The phase distribution in concrete materials strongly affects its material properties. It is important to identify the spatial distribution of void in concrete because the void in concrete materials affects mechanical behavior and permeability significantly. Therefore, a proper method to describe the void distribution of a material is needed. In this research, CT(computed tomography) is used to examine and to quantify the void distribution of porous concrete specimens. 3D concrete digital specimens are created by subsequent stacking of 2D cross-sectional images from CT. Then, probability distribution functions such as two-point correlation, lineal-path and two-point cluster functions are used for void distribution characterization. It is confirmed that probability distribution functions obtained from CT images are effective in characterizing void distributions including the anisotropy and percolation.

• The Korean Journal of Applied Statistics
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• v.26 no.5
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• pp.759-766
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• 2013

The paper examines several classes of probability distributions with heavy tails. An (asymptotic) expression for tail probability needs to be known to understand which class a given probability distribution belongs to. It is usually not easy to get expressions for tail probabilities since most absolutely continuous probability distributions are specified by probability density functions and not by distribution functions. The paper proposes a method to obtain asymptotic expressions for tail probabilities using only probability density functions. Some examples are given to illustrate the proposed method.

• Kyungpook Mathematical Journal
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• v.45 no.3
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• pp.423-431
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• 2005

Some recent inequalities for expectation and cumulative distribution function are improved.

• Journal of The Korean Society of Agricultural Engineers
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• v.55 no.5
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• pp.49-58
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• 2013

Appropriate random variables and probability density functions based on statistical analysis should be defined to execute reliability analysis. Most studies have focused on only normal distributions or assumed that the variables showing non-normal characteristics follow the normal distributions. In this study, the reliability problem with non-normal probability distribution was dealt with using the convolution method in the case that the integration domains of variables are limited to a finite range. The results were compared with the traditional method (linear transformation of normal distribution) and Monte Carlo simulation method to verify that the application was in good agreement with the characteristics of probability density functions with peak shapes. However it was observed that the reproducibility was slightly reduced down in the tail parts of density function.