• Journal of Forest and Environmental Science
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• v.34 no.6
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• pp.451-456
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• 2018

The use of single component distribution to describe the irregular stand structure of degraded forest often lead to bias. Such biasness can be overcome by the application of finite mixture distribution. Therefore, in this study, finite mixture distribution was used to characterise the irregular stand structure of the Gmelina arborea plantation in Omo forest reserve. Thirty plots, ten each from the three stands established in 1984, 1990 and 2005 were used. The data were pooled per stand and fitted. Four finite mixture distributions including normal mixture, lognormal mixture, gamma mixture and Weibull mixture were considered. The method of maximum likelihood was used to fit the finite mixture distributions to the data. Model assessment was based on negative loglikelihood value ($-{\Lambda}{\Lambda}$), Akaike information criterion (AIC), Bayesian information criterion (BIC) and root mean square error (RMSE). The results showed that the mixture distributions provide accurate and precise characterisation of the irregular diameter distribution of the degraded Gmelina arborea stands. The $-{\Lambda}{\Lambda}$, AIC, BIC and RMSE values ranged from -715.233 to -348.375, 703.926 to 1433.588, 718.598 to 1451.334 and 3.003 to 7.492, respectively. Their performances were relatively the same. This approach can be used to describe other irregular forest stand structures, especially the multi-species forest.

• Journal of Forest and Environmental Science
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• v.36 no.1
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• pp.7-16
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• 2020

Tree size distribution modelling is an integral part of forest management. Most distribution yield systems rely on some flexible probability models. In this study, a simple finite mixture of two components two-parameter Weibull distribution was compared with complex four-parameter distributions in terms of their fitness to predict tree size distribution of teak (Tectona grandis Linn f) plantations. Also, a system of equation was developed using Seemingly Unrelated Regression wherein the size distributions of the stand were predicted. Generalized beta, Johnson's SB, Logit-Logistic and generalized Weibull distributions were the four-parameter distributions considered. The Kolmogorov-Smirnov test and negative log-likelihood value were used to assess the distributions. The results show that the simple finite mixture outperformed the four-parameter distributions especially in stands that are bimodal and heavily skewed. Twelve models were developed in the system of equation-one for predicting mean diameter, seven for predicting percentiles and four for predicting the parameters of the finite mixture distribution. Predictions from the system of equation are reasonable and compare well with observed distributions of the stand. This simplified mixture would allow for wider application in distribution modelling and can also be integrated as component model in stand density management diagram.

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.4
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• pp.145-153
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• 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.

• Communications for Statistical Applications and Methods
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• v.21 no.6
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• pp.501-512
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• 2014

Stylized facts on asset return are fat-tail, asymmetry, volatility clustering and structure changes. This paper simultaneously captures these characteristics by introducing a multi-regime models: Finite mixture distribution and regime switching GARCH model. Analyzing the daily KOSPI return from $4^{th}$ January 2000 to $30^{th}$ June 2014, we find that a two-component mixture of t distribution is a good candidate to describe the shape of the KOSPI return from unconditional and conditional perspectives. Empirical results suggest that the equality assumption on the shape parameter of t distribution yields better discrimination of heterogeneity component in return data. We report the strong regime-dependent characteristics in volatility dynamics with high persistence and asymmetry by employing a regime switching GJR-GARCH model with t innovation model. Compared to two sub-samples, Pre-Crisis (January 2003 ~ December 2007) and Post-Crisis (January 2010 ~ June 2014), we find that the degree of persistence in the Pre-Crisis is higher than in the Post-Crisis along with a strong asymmetry in the low-volatility (high-volatility) regime during the Pre-Crisis (Post-Crisis).

• 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.

• 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 the Korean Society of Safety
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• v.28 no.6
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• pp.6-10
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• 2013

A numerical reproducibility of the backdraft phenomena in a compartment was investigated. The prediction performance of two combustion models, the mixture fraction and finite chemistry models, were tested for the backdraft phenomena using the FDS code developed by the NIST. The mixture fraction model could not predict the flame propagation in a fuel-air mixture as well as the backdraft phenomena. However, the finite chemistry model predicted the flame propagation in the mixture inside a tube reasonably. In addition, the finite chemistry model predicted well the backdraft phenomena in a compartment qualitatively. The flame propagation inside the compartment, fuel and oxygen distribution and explosive fire ball behavior were well simulated with the finite chemistry model. It showed that the FDS adopted with the finite chemistry model can be an effective simulation tool for the investigation of backdraft in a compartment.

• Journal of the Korean Data and Information Science Society
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• v.9 no.2
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• pp.289-298
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• 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.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.6
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• pp.725-730
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• 2007

Gray-level histogram-based threshold selection methods such as Otsu's method, Huang and Wang's method, and etc. have been widely used for the threshold selection in image processing. They are simple and effective, but take too much time to determine the optimal multilevel threshold values as the number of thresholds are increased. In this paper, we measure correlation between gray-levels by using the Gaussian function and define a Gaussian-type finite mixture distribution which is combination of the Gaussian distribution function with the gray-level histogram, and propose a fast and effective threshold selection method using it. We show the effectiveness of the proposed through experimental results applied it to three images and the efficiency though comparison of the computational complexity of the proposed with that of Otsu's method.

• Clinical and Experimental Pediatrics
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• v.48 no.11
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• pp.1179-1186
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• 2005

Purpose : A universal standard of the birth weight for gestational age cannot be made since girth weight distribution varies with race and other sociodemographic factors. This report aims to establish the birth weight distribution curve by gestational age, specific for Korean live births. Methods : We used the national birth certificate data of all live births in Korea from January 2001 to December 2003; for live births with gestational ages 24 weeks to 44 weeks(n=1,509,763), we obtained mean birth weigh, standard deviation and 10th, 25th, 50th, 75th and 90th percentile values for each gestational age group by one week increment. Then, we investigated the birth weight distribution of each gestational age group by the normal Gaussian model. To establish final standard values of Korean birth weight distribution by gestational age, we used the finite mixture model to eliminate erroneous birth slights for respective gestational ages. Results : For gestational ages 28 weeks 32 weeks, birth weight distribution showed a biologically implausible skewed tail or bimodal distribution. Following correction of the erroneous distribution by using the finite mixture model, the constructed curve of birth weight distribution was compared to those of other studies. The Korean birth weight percentile values were generally lower than those for Norwegians and North Americans, particularly after 37 weeks of gestation. The Korean curve was similar to that of Lubchenco both 50th and 90th percentiles, but generally the Korean curve had higher 10th percentile values. Conclusion : This birth weight distribution curve by gestational age is based on the most recent and the national population data compared to previous studies in Korea. We hope that for Korean infants, this curve will help clinicians in defining and managing the large for gestational age infants and also for infants with intrauterine growth retardation.