• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.785-794
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• 2006

Suggested is an EM algorithm for estimation in mixture of shifted Poisson distributions with known shift parameters. For this type of mixture distribution, we have to utilize values of shift parameters to determine whether each of data belongs to some component distribution. We propose a method of estimating values of component information and then follow typical EM methodology. Simulation results show that the algorithm provides reasonable performance for the distribution.

• The Journal of The Korea Institute of Intelligent Transport Systems
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• v.22 no.4
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• pp.35-47
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• 2023

Various single probability distributions have been used to represent time headway distributions. However, it has often been difficult to explain the time headway distribution as a single probability distribution on site. This study used the EM algorithm, which is one of the maximum likelihood estimations, for the parameters of combined mixture distributions with a certain relationship between two normal distributions for the time headway of vehicles. The time headway distribution of vehicle arrival is difficult to represent well with previously known single probability distributions. But as a result of this analysis, it can be represented by estimating the parameters of the mixture probability distribution using the EM algorithm. The result of a goodness-of-fit test was statistically significant at a significance level of 1%, which proves the reliability of parameter estimation of the mixture probability distribution using the EM algorithm.

• 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.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.

• 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.

• The Korean Journal of Applied Statistics
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• v.28 no.5
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• pp.847-858
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• 2015

Deep-sea fishery in the Antarctic Ocean has been actively progressed by the developed countries including Korea. In order to prevent the environmental destruction of the Antarctic Ocean, related countries have established the Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR) and have monitored any illegal unreported or unregulated fishing. Fishing of tooth fish, an expensive fish, in the Antarctic Ocean has increased recently and high catches per unit effort (CPUE) of fishing boats, which is suspicious for an illegal activity, have been frequently reported. The data of CPUEs in a fishing area of the Antarctic Ocean often show an extreme Distribution or a mixture of two extreme distributions. This paper proposes an algorithm to detect an outlier of CPUEs by using the mixture of two extreme distributions. The parameters of the mixture distribution are estimated by the EM algorithm. Log likelihood value and posterior probabilities are used to detect an outlier. Experiments show that the proposed algorithm to detect outlier of the data can be adopted instead of simple criteria such as a CPUE is greater than 1.

• Environmental and Resource Economics Review
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• v.11 no.2
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• pp.321-333
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• 2002

Approximating bottled water consumption distribution is complicated by zero observations in the sample. To deal with the zero observations, a mixture model of bottled water consumption distributions is proposed and applied to allow a point mass at zero. The bottled water consumption 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 bottled water consumption survey data. The mixture model can easily capture the common bimodality feature of the bottled water consumption distribution. In addition, when covariates were added to the model, it was found that the probability that a household has non-consumption significantly varies with some variables.

• Journal of the Korean Data and Information Science Society
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• v.17 no.4
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• pp.1209-1217
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• 2006

For the mixture of shifted Poisson distributions, a method of parameter estimation is proposed. The range of the shifted parameters are estimated first and for each shifted parameter set EM algorithm is applied to estimate the other parameters of the distribution. Among the estimated parameter sets, one with minimum likelihood for given data is to be set as the final estimate. In simulation experiments, the suggested estimation method shows to have a good performance.

• 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 the Korean Data and Information Science Society
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• v.21 no.2
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• pp.219-229
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• 2010

There have been many researches on the risk management due to rapid increase of various risk factors for financial assets. Aa a method for comprehensive risk management, Value at Risk (VaR) is developed. For estimation of VaR, it is important task to solve the problem of asymmetric distribution of the return rate with heavy tail. Most real distributions of the return rate have high positive kurtosis and low negative skewness. In this paper, some alternative distributions are used to be fitted to real distributions of the return rate of financial asset. And estimates of VaR obtained by using these fitting distributions are compared with those obtained from real distribution. It is found that normal mixture distribution is the most fitted where its skewness and kurtosis of practical distribution are close to real ones, and the VaR estimation using normal mixture distribution is more accurate than any others using other distributions including normal distribution.