• Journal of the Korean Data and Information Science Society
• /
• 제9권2호
• /
• pp.289-298
• /
• 1998

We investigate the distribution of likelihood ratio test(LRT) of null hypothesis a sample is from single gamma with unknown shape and scale against the alternative hypothesis a sample is from a mixture of two gammas, each with unknown scale and unknown (but equal) scale. To obtain stable maximum likelihood estimates(MLE) of a mixture of two gamma distributions, the EM(Dempster, Laird, and Robin(1977))and Modified Newton(Jensen and Johansen(1991)) algorithms were implemented. Based on EM, we made a simple structure likelihood equation for each parameter and could obtain stable solution by Modified Newton Algorithms. Simulation study was conducted to investigate the distribution of LRT for sample size n = 25, 50, 75, 100, 50, 200, 300, 400, 500 with 2500 replications. To determine the small sample distribution of LRT, I considered the model of a gamma distribution with shape parameter equal to 1 + f(n) and scale parameter equal to 2. The simulation results indicate that the null distribution is essentially invariant to the value of the shape parameter. Modeling of the null distribution indicates that it is well approximated by a gamma distribution with shape parameter equal to the quantity $0.927+1.18/\sqrt{n}$ and scale parameter equal to 2.16.

• International Journal of Reliability and Applications
• /
• 제6권2호
• /
• pp.101-115
• /
• 2005

This article provides a new class of multivariate linear failure rate distributions where every component is a mixture of linear failure rate distribution. The new class includes several multivariate and bivariate models including Marslall and Olkin type. The approach in this paper is based on the introducing a linear failure rate distributed latent random variable. The distribution of minimum in a competing risk model is discussed.

• International Journal of Reliability and Applications
• /
• 제7권1호
• /
• pp.55-69
• /
• 2006

This paper presents a new class of multivariate distributions with Pareto where dependence among the components is characterized by a latent random variable. The new class includes several multivariate and bivariate models of Marshall and Olkin type. It is found the bivariate distribution with Pareto is positively quadrant dependent and its mixture. Some important structural properties of the bivariate distributions with Pareto are discussed. The distribution of minimum in a competing risk Pareto model is derived.

• Journal of the Korean Data and Information Science Society
• /
• 제17권3호
• /
• pp.785-794
• /
• 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.

• 자원ㆍ환경경제연구
• /
• 제11권2호
• /
• pp.321-333
• /
• 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.

• 기술혁신학회지
• /
• 제8권3호
• /
• pp.887-910
• /
• 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.

• ETRI Journal
• /
• 제43권1호
• /
• pp.74-81
• /
• 2021

The mixture model is a very powerful and flexible tool in clustering analysis. Based on the Dirichlet process and parsimonious Gaussian distribution, we propose a new nonparametric mixture framework for solving challenging clustering problems. Meanwhile, the inference of the model depends on the efficient online variational Bayesian approach, which enhances the information exchange between the whole and the part to a certain extent and applies to scalable datasets. The experiments on the scene database indicate that the novel clustering framework, when combined with a convolutional neural network for feature extraction, has meaningful advantages over other models.

• 한국경영과학회지
• /
• 제28권4호
• /
• pp.145-153
• /
• 2003

In this Paper, we examine the limiting distributional behaviour of extreme values of mixed Erlang random variables. We show that, in the finite mixture of Erlang distributions, the component distribution with an asymptotically dominant tail has a critical effect on the asymptotic extreme behavior of the mixture distribution and it converges to the Gumbel extreme-value distribution. Normalizing constants are also established. We apply this result to characterize the asymptotic distribution of maxima of sojourn times in M/M/s queuing system. We also show that Erlang mixtures with continuous mixing may converge to the Gumbel or Type II extreme-value distribution depending on their mixing distributions, considering two special cases of uniform mixing and exponential mixing.

• 한국ITS학회 논문지
• /
• 제22권4호
• /
• pp.35-47
• /
• 2023

그동안 차두시간분포를 나타내는 확률분포로 음지수분포, Erlang 분포, 정규분포 등 다양한 단일확률분포들이 사용되어져 왔다. 그러나, 실제 도로에서 차두시간분포의 조사결과는 단일확률분포로서 설명하기 어려운 경우가 있었다. 본 연구는 차량의 차두시간에 대해 두 개의 정규분포가 일정한 관련성을 가지고 결합된 복합확률분포의 파라메타에 대해 최우추정법 중 하나인 EM 알고리즘을 이용하여 추정하는 접근방법을 시도하였다. 이에 대한 분석결과 기존에 알려진 단일확률분포로서 잘 설명되기 어려웠던 차량도착 차두시간 분포를 EM 알고리즘을 이용하여 복합확률분포의 파라메타를 추정하여 설명하였다. χ² test 적합도 검정결과, 유의수준 1%에서 통계학적으로 유의성이 확보되어 EM 알고리즘을 이용한 복합확률분포의 파라메타 추정의 신뢰성이 입증되는 것으로 분석되었다.

• 해양환경안전학회지
• /
• 제21권3호
• /
• pp.253-258
• /
• 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.