• Ocean Systems Engineering
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• v.12 no.3
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• pp.267-284
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• 2022

A subsea pipeline designed across active shipping lane prones to failure against external interferences such as anchorage activities, hence risk assessment is essential. It requires quantifying the geometric probability derived from ship traffic distribution based on Automatic Identification System (AIS) data. The actual probability density function from historical vessel traffic data is ideal, as for rapid assessment, conceptual study, when the AIS data is scarce or when the local vessels traffic are not utilised with AIS. Recommended practices suggest the probability distribution is assumed as a single peak Gaussian. This study compares several fitted Gaussian distributions and Monte Carlo simulation based on actual ship traffic data in main ship direction in an active shipping lane across a subsea pipeline. The results shows that a Gaussian distribution with five peaks is required to represent the ship traffic data, providing an error of 0.23%, while a single peak Gaussian distribution and the Monte Carlo simulation with one hundred million realisation provide an error of 1.32% and 0.79% respectively. Thus, it can be concluded that the multi-peak Gaussian distribution can represent the actual ship traffic distribution in the main direction, but it is less representative for ship traffic distribution in other direction. The geometric probability is utilised in a quantitative risk assessment (QRA) for subsea pipeline against vessel anchor dropping and dragging and vessel sinking.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.3
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• pp.130-136
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• 2010

In this study, we propose a new method for generating candidate solutions based on both the Cauchy and the Gaussian probability distributions in order to use the merit of the solutions generated by these distributions. The Cauchy probability distribution has larger probability in the tail region than the Gaussian distribution. Thus, the Cauchy distribution can yield higher probabilities of generating candidate solutions of large-varied variables, which in turn has an advantage of searching wider area of variable space. On the contrary, the Gaussian distribution can yield higher probabilities of generating candidate solutions of small-varied variables, which in turn has an advantage of searching deeply smaller area of variable space. In order to compare and analyze the performance of the proposed method against the conventional method, we carried out experiments using benchmarking problems of real valued functions. From the result of the experiment, we found that the proposed method based on the Cauchy and the Gaussian distributions outperformed the conventional one for most of benchmarking problems, and verified its superiority by the statistical hypothesis test.

• 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.

• East Asian mathematical journal
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• v.39 no.5
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• pp.537-547
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• 2023

In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

• 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.

• Wind and Structures
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• v.37 no.3
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• pp.211-227
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• 2023

To investigate the non-Gaussian feature of fluctuating wind pressures on rectangular high-rise buildings, wind tunnel tests were conducted on scale models with side ratios ranging from 1/9~9 in an open exposure for various wind directions. The high-order statistical moments, time histories, probability density distributions, and peak factors of pressure fluctuations are analyzed. The mixed normal-Weibull distribution, Gumbel-Weibull distribution, and lognormal-Weibull distribution are adopted to fit the probability density distribution of different non-Gaussian wind pressures. Zones of Gaussian and non-Gaussian are classified for rectangular buildings with various side ratios. The results indicate that on the side wall, the non-Gaussian wind pressures are related to the distance from the leading edge. Apart from the non-Gaussianity in the separated flow regions noted by some literature, wind pressures behind the area where reattachment happens present non-Gaussian nature as well. There is a new probability density distribution type of non-Gaussian wind pressure which has both long positive and negative tail found behind the reattachment regions. The correlation coefficient of wind pressures is proved to reflect the non-Gaussianity and a new method to estimate the mean reattachment length of rectangular high-rise building side wall is proposed by evaluating the correlation coefficient. For rectangular high-rise buildings, the mean reattachment length calculated by the correlation coefficient method along the height changes in a parabolic shape. Distributions of Gaussian and non-Gaussian wind pressures vary with side ratios. It is inappropriate to estimate the extreme loads of wind pressures using a fixed peak factor. The trend of the peak factor with side ratios on different walls is given.

• 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).

• Journal of Positioning, Navigation, and Timing
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• v.9 no.1
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• pp.23-31
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• 2020

It is essential to estimate the vehicle localization for an autonomous safety driving. In particular, since LIDAR provides precise scan data, many studies carried out to estimate the vehicle localization using LIDAR and pre-generated map. The road marking always exists on the road because of provides driving information. Therefore, it is often used for map information. In this paper, we propose to generate the Gaussian mixture map based on road-marking information and localization method using this map. Generally, the probability distributions map stores the single Gaussian distribution for each grid. However, single resolution probability distributions map cannot express complex shapes when grid resolution is large. In addition, when grid resolution is small, map size is bigger and process time is longer. Therefore, it is difficult to apply the road marking. On the other hand, Gaussian mixture distribution can effectively express the road marking by several probability distributions. In this paper, we generate Gaussian mixture map and perform vehicle localization using Gaussian mixture map. Localization performance is analyzed through the experimental result.

• The Korean Journal of Applied Statistics
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• v.26 no.4
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• pp.611-622
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• 2013

Mudholkar and Tian (2002) proposed an entropy-based test of fit for the inverse Gaussian distribution; however, the test can be applied to only the composite hypothesis of the inverse Gaussian distribution with an unknown location parameter. In this paper, we propose an entropy-based goodness-of-fit test for an inverse Gaussian distribution that can be applied to the composite hypothesis of the inverse Gaussian distribution as well as the simple hypothesis of the inverse Gaussian distribution with a specified location parameter. The proposed test is based on the probability integration transformation. The critical values of the test statistic estimated by simulations are presented in a tabular form. A simulation study is performed to compare the proposed test under some selected alternatives with Mudholkar and Tian (2002)'s test in terms of power. The results show that the proposed test has better power than the previous entropy-based test.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.49.1-49
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• 2001

The skin color model is a very important concept in face detection, face recognition and face tracking. Usually, this model is obtained by estimating a probability density function of skin color distribution. In many cases, it is assumed that the underlying density function follows a Gaussian distribution. In this paper, a new method for non-parametric estimation of the probability density function, by using feed-forward neural network, is used to estimate the underlying skin color model. By using this method, the resulting skin color model is better than the Gaussian estimation and substantially approaches the real distribution. Applications to face detection and face ...