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

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2007.11a
• /
• pp.469-473
• /
• 2007

For the quantitative analysis of inclusion using OES data, separating of noise and inclusion is needed. In previous methods assuming that noises come from a normal distribution, intensity levels beyond a specific threshold are determined as inclusions. However, it is not possible to classify inclusions in low intensity region using this method, even though every inclusion is an element of some chemical compound. In this paper, we assume that distribution of OES data is a Gaussian mixture and estimate the parameters of the mixture model using EM algorithm. Then, we calculate mixing ratio of noise and inclusion using these parameters to separate noise and inclusion.

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

• Journal of the Korean Data and Information Science Society
• /
• v.28 no.2
• /
• pp.251-260
• /
• 2017

The option pricing of Black와 Scholes (1973) and Merton (1973) has been widely reported to fail to reflect the time varying volatility of financial time series in many real applications. For example, Duan (1995) proposed GARCH option pricing method through Monte Carlo simulation. However, financial time series is known to follow a fat-tailed and leptokurtic probability distribution, which is not explained by Duan (1995). In this paper, in order to overcome such defects, we proposed the option pricing method based on GARCH models with normal mixture errors. According to the analysis of KOSPI200 option price data, the option pricing based on GARCH models with normal mixture errors outperformed the option pricing based on GARCH models with normal errors in the unstable period with high volatility.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.28 no.3
• /
• pp.171-176
• /
• 2016

The distribution shapes of air and water temperatures are basic and essential information, which determine the frequency patterns of their occurrence. It is also very useful to understand the changes in long-term air and water temperatures with respect to climate change. The typical distribution shapes of air and water temperatures cannot be well fitted using widely used/accepted normal distributions because their shapes show multimodal distributions. In this study, Gaussian mixture distributions and kernel distributions are suggested as the more suitable models to fit their distribution shapes. Based on the results, the tail shape exhibits different patterns. The tail is long in higher temperature regions of water temperature distribution and in lower temperature regions of air temperature distribution. These types of shape comparisons can be useful to identify the patterns of long-term air and water temperature changes and the relationship between air and water temperatures. It is nearly impossible to identify change patterns using only mean-temperatures and normal distributions.

• Journal of Integrative Natural Science
• /
• v.6 no.4
• /
• pp.251-255
• /
• 2013

For the mean vector of a p-variate normal distribution ($p{\geq}4$), the optimal estimation within the class of modified James-Stein type decision rules under the quadratic loss is given when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-\bar{\theta}1{\parallel}$ it known.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.2
• /
• pp.487-493
• /
• 2015

Time series data sometimes show violation of normal assumptions. For cases where the assumption of normality is untenable, more exible models can be adopted to accommodate heavy tails. The exponential power distribution (EPD) is considered as possible candidate for errors of time series model that may show violation of normal assumption. Besides, the use of exible models for errors like EPD might be able to conduct the robust analysis. In this paper, we especially consider EPD as the exible distribution for errors of autoregressive models. Also, we represent this distribution as scale mixture of uniform and this form enables efficient Bayesian estimation via Markov chain Monte Carlo (MCMC) methods.

• Journal of Advanced Marine Engineering and Technology
• /
• v.41 no.1
• /
• pp.111-117
• /
• 2017

The arrival time of rescue ships is very important in the event of distress. This paper presents the development of experimental data to calculate the arrival time of rescue ships. The ship's traffic probability distribution was used. Mokpo Port was selected as the area of study, and AIS data for a 1 year period were used. For the ship's traffic probability distribution, a gateline was established. The lateral range distribution was calculated and fitted to the normal distribution and two Gaussian mixture distributions (GMD2), and each parameter was extracted. After the locations of ${\mu}$, ${\mu}{\pm}1{\sigma}$ of the normal distribution and ${\mu}_1$ of the two Gaussian mixture distribution(GMD2) were set as waypoints, the location and probability were determined. A scenario was established in relation to each type of parameter. Thus, the arrival time can be calculated.

• 한국데이터정보과학회:학술대회논문집
• /
• 2004.04a
• /
• pp.127-130
• /
• 2004

혼합정규분포에서 얻어진 히스토그램 자료에서 모수의 추정은 EM 알고리즘 혹은 스프라인 방법이 흔히 이용되고 있다. 본 논문에서는 히스토그램 자료를 비선형회귀모형으로 적합하는 방법을 제시하고, 시뮬레이션으로 제시된 방법과 EM 알고리즘 방법을 비교하였다.

• Communications for Statistical Applications and Methods
• /
• v.25 no.6
• /
• pp.633-645
• /
• 2018

Gaussian error distributions are a common choice in traditional regression models for the maximum likelihood (ML) method. However, this distributional assumption is often suspicious especially when the error distribution is skewed or has heavy tails. In both cases, the ML method under normality could break down or lose efficiency. In this paper, we consider the log-concave and Gaussian scale mixture distributions for error distributions. For the log-concave errors, we propose to use a smoothed maximum likelihood estimator for stable and faster computation. Based on this, we perform comparative simulation studies to see the performance of coefficient estimates under normal, Gaussian scale mixture, and log-concave errors. In addition, we also consider real data analysis using Stack loss plant data and Korean labor and income panel data.