• 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.

• Journal of Energy Engineering
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• v.23 no.3
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• pp.36-41
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• 2014

The world's overall need for natural gas (NG) has been growing up fast, especially in the residential sector. The better the estimation of residential NG consumption (RNGC) distribution, the better decision-making for a residential NG policy such as pricing, demand estimation, management options and so on. Approximating the distribution of RNGC is complicated by zero observations in the sample. To deal with the zero observations by allowing a point mass at zero, a mixture model of RNGC distributions is proposed and applied. The RNGC distribution is specified as a mixture of two distributions, one with a point mass at zero and the other with full support on the positive half of the real line. The model is empirically verified for household RNGC survey data collected in Korea. The mixture model can easily capture the common bimodality feature of the RNGC distribution. In addition, when covariates were added to the model, it was found that the probability that a household has non-expenditure significantly varies with some variables. Finally, the goodness-of-fit test suggests that the data are well represented by the mixture model.

• Journal of Korea Technology Innovation Society
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• v.8 no.3
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• pp.887-910
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• 2005

This paper attempts to approximate the distribution function for the number of innovation activities (NIA). To this end, the dataset of 2002 Korean Innovation Survey (KIS 2002) published by Science and Technology Policy Institute is used. To deal with zero NTI values given by a considerable number of firms in the KIS 2002 survey, a mixture model of distributions for NIA is applied. The NIA is specified as a mixture of two distributions, one with a point mass at zero and the other with full support on the positive half of the real line. The model was empirically verified for the KIS 2002 data. The mixture model can easily capture the common bimodality feature of the NIA distribution. In addition, when covariates were added to the mixture model, it was found that the probability that a firm has zero NIA significantly varies with some variables.

• Smart Structures and Systems
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• v.21 no.5
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• pp.591-600
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• 2018

The probabilistic characterization of wind field characteristics is a significant task for fatigue reliability assessment of long-span railway bridges in wind-prone regions. In consideration of the effect of wind direction, the stochastic properties of wind field should be represented by a bivariate statistical model of wind speed and direction. This paper presents the construction of the bivariate model of wind speed and direction at the site of a railway arch bridge by use of the long-term structural health monitoring (SHM) data. The wind characteristics are derived by analyzing the real-time wind monitoring data, such as the mean wind speed and direction, turbulence intensity, turbulence integral scale, and power spectral density. A sequential quadratic programming (SQP) algorithm-based finite mixture modeling method is proposed to formulate the joint distribution model of wind speed and direction. For the probability density function (PDF) of wind speed, a double-parameter Weibull distribution function is utilized, and a von Mises distribution function is applied to represent the PDF of wind direction. The SQP algorithm with multi-start points is used to estimate the parameters in the bivariate model, namely Weibull-von Mises mixture model. One-year wind monitoring data are selected to validate the effectiveness of the proposed modeling method. The optimal model is jointly evaluated by the Bayesian information criterion (BIC) and coefficient of determination, $R^2$. The obtained results indicate that the proposed SQP algorithm-based finite mixture modeling method can effectively establish the bivariate model of wind speed and direction. The established bivariate model of wind speed and direction will facilitate the wind-induced fatigue reliability assessment of long-span bridges.

• Journal of Korea Multimedia Society
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• v.7 no.11
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• pp.1531-1539
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• 2004

In this paper, we propose an efficient method for locating human lips. Based on Point Distribution Model and Principle Component Analysis, a lip shape model is built. Lip boundary model is represented based on the concatenated gray level distribution model. We calculate the distribution of shape parameters using Gaussian mixture. The problem to locate lip is simplified as the minimization problem of matching object function. The Down Hill Simplex Algorithm is used for the minimization with Gaussian Mixture for setting initial condition and refining estimate of lip shape parameter, which can refrain iteration from converging to local minima. The experiments have been performed for many images, and show very encouraging result.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.500-506
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• 2017

In 2014, ISO 55000s has been enacted and the power plant asset management is becoming a hot issue for all over the world. The asset management system is being developed as a combination of CBM(Condition Based Maintenance) and RCM(Reliability Centered Maintenance). Therefore, the research on the calculation of the failure rate which is the most basic index of RCM is actively carried out. The failure rate calculation has been going on for a long time, and the most widely used probability distribution is the Weibull distribution. In the Weibull distribution, the failure rate function is determined in three types according to the value of the shape parameter. However, the Weibull distribution has a limitation that it is difficult to apply it when the trend of failure rate changes-such as bathtub curves. In this paper, the failure rate is calculated using the mixture Weibull distribution which can appropriately express the change of the shape of the failure rate. Based on these results, we propose the necessity and validity of applying mixture Weibull distribution.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.987-994
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• 2011

From the point view of credit evaluation whose population is divided into the default and non-default state, two methods are considered to estimate conditional distribution functions: one is to estimate under the assumption that the data is followed the mixture normal distribution and the other is to use the kernel density estimation. The parameters of normal mixture are estimated using the EM algorithm. For the kernel density estimation, five kinds of well known kernel functions and four kinds of the bandwidths are explored. In addition, the corresponding ROC functions are obtained based on the estimated distribution functions. The goodness-of-fit of the estimated distribution functions are discussed and the performance of the ROC functions are compared. In this work, it is found that the kernel distribution functions shows better fit, and the ROC function obtained under the assumption of normal mixture shows better performance.

• International Journal of Reliability and Applications
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• v.10 no.2
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• pp.63-79
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• 2009

A new bivariate linear failure rate distribution is introduced through a shock model. It is proved that the marginal distributions of this new bivariate distribution are linear failure rate distributions. The joint moment generating function of the bivariate distribution is derived. Mixtures of bivariate linear failure rate distributions are also discussed. Application to a real data is given.

• Smart Structures and Systems
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• v.17 no.6
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• pp.1087-1105
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• 2016

Traffic load and volume is one of the most important physical quantities for bridge safety evaluation and maintenance strategies formulation. This paper aims to conduct the statistical analysis of traffic volume information and the multimodal modeling of gross vehicle weight (GVW) based on the monitoring data obtained from the weigh-in-motion (WIM) system instrumented on the arch Jiubao Bridge located in Hangzhou, China. A genetic algorithm (GA)-based mixture parameter estimation approach is developed for derivation of the unknown mixture parameters in mixed distribution models. The statistical analysis of one-year WIM data is firstly performed according to the vehicle type, single axle weight, and GVW. The probability density function (PDF) and cumulative distribution function (CDF) of the GVW data of selected vehicle types are then formulated by use of three kinds of finite mixed distributions (normal, lognormal and Weibull). The mixture parameters are determined by use of the proposed GA-based method. The results indicate that the stochastic properties of the GVW data acquired from the field-instrumented WIM sensors are effectively characterized by the method of finite mixture distributions in conjunction with the proposed GA-based mixture parameter identification algorithm. Moreover, it is revealed that the Weibull mixture distribution is relatively superior in modeling of the WIM data on the basis of the calculated Akaike's information criterion (AIC) values.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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• pp.389-396
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• 2009

Approximations for the null distribution of a test statistic arising in multivariate analysis to test homogeneity of variances and a mixture of two beta distributions by making use of a product of beta baseline density function and a polynomial adjustment, so called beta-polynomial density approximant, are discussed. Explicit representations of density and distribution approximants of interest in each case can easily be obtained. Beta-polynomial density approximants produce good approximation over the entire range of the test statistic and also accommodate even the bimodal distribution using an artificial example of a mixture of two beta distributions.