• Journal of Forest and Environmental Science
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• 제34권6호
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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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• 제36권1호
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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.

• 한국경영과학회지
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• 제28권4호
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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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• 제21권6호
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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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• 제17권6호
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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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• 제21권5호
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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.

• 한국안전학회지
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• 제28권6호
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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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• 제9권2호
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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.

• 한국지능시스템학회논문지
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• 제17권6호
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• pp.725-730
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• 2007

Otsu의 임계값 결정법, Huang와 Wang의 임계값 결정법 등을 포함한 그레이 레벨 히스토그램에 기반한 임계값 결정법은 영상처리 분야에서 널리 사용되어져 왔다. 이들 기법들은 그 효용성이 뛰어남에도 불구하고 하나의 임계값이 아닌 다중 임계값을 추출하는 경우 많은 연산 시간이 소요되는 단점을 가지고 있다. 즉, 임계값의 개수가 늘어남에 따라 연산 복잡도 역시 기하급수적으로 증가하게 된다 본 논문에서는 가우시안 함수를 이용하여 그레이 레벨간의 상관관계를 측정하고, 가우시안 분포함수와 그레이 레벨의 히스토그램을 결합한 가우시안형 유한 혼합 분포를 이용하여 연산 복잡도가 단순하며 효용성 있는 임계값 결정법을 제안한다. 다수의 영상에 제안한 기법을 적용한 모의실험을 통하여 효용성을 확인하고, Otsu의 임계값 결정법과 제안한 기법의 연산 복잡도 비교를 통해서 제안한 임계값 결정법의 효율성을 보인다.

• Clinical and Experimental Pediatrics
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• 제48권11호
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• pp.1179-1186
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• 2005

목 적 : 재태 연령에 따른 신생아 출생체중의 정상치를 아는 것은 자궁내 발육부전과 과출생 체중아를 진단하여 의사들은 고위험 신생아를 조기에 진단하고 치료하여 이들의 유병률과 사망률을 줄일 수 있고, 의료정책 입안자들은 이들에 대한 적절한 의료서비스의 개발과 건강관리 프로그램을 개발하고 시행하는데 도움을 줄 수 있다. 이에 저자들은 우리나라의 재태 연령에 따른 출생체중의 기준치를 구하고자 본 연구를 시행하였다. 방 법 : 2001년 1월 1일부터 2003년 12월 31일까지 3년간 통계청의 인구동태자료 중 출생 자료에 기록되어 있는 1,552,375명 중 재태 연령이 24주에서 44주 사이의 단태아 1,509,763명을 대상으로 재태 연령에 따른 평균값과 표준편차를 구하고 10, 25, 50, 75, 90 백분위수를 구하였다. 또한 각 재태 연령별 분포곡선이 정규분포를 따르는지 알아보았다. 이중 정규분포를 따르지 않거나 쌍봉형을 나타내는 재태 연령에서 유한 혼합 모델을 이용하여 오류의 값을 제거하고 다시 평균과 표준편차 그리고 10, 25, 50, 75, 90 백분위수를 구하고 이에 따른 곡선을 그렸다. 결 과 : 원시자료를 통해 얻은 재태 연령에 따른 출생체중 곡선은 27주에서 32주 사이에 심한 혹이 나타난다. 이에 따라 재태 연령별 출생체중의 분포를 그렸을 때 24주에서 27주까지는 우측으로 긴 꼬리를 가지는 치우친 곡선을 보였고 28주에서 32주까지는 상봉형의 곡선을 보였다. 그리고 그 이후에는 거의 정규 분포를 따르는 곡선을 보였다. 이는 33주 미만에서 재태 연령의 기록에 오류가 있음을 나타내는 것으로 저자들은 유한 혼합 모델을 이용해서 재태 연령별 출생체중 분포를 분석한 후 오류의 부분을 제거 후 재태 연령에 따른 출생체중 곡선을 완성하였다. 이렇게 완성된 출생체중 곡선은 Lubchenco 등의 결과에 비해 10 백분위수에서 높은 값을 보였고 노르웨이나 북미의 연구 결과에 비해서는 전반적으로 낮은 값을 보였다. 결 론 : 본 연구에서 얻은 재태 연령에 의한 출생체중의 기준치와 곡선은 3년간 우리나라의 출생아 전수를 대상으로 오류를 객관적인 기준에 의해 제거하여 만든 것이다. 그러므로 우리나라를 대표하난 신생아의 재태 연령에 의한 출생체중의 기준 및 자궁내 발육부전이나 과출생 체중아의 진단의 기준으로 사용 할 수 있으리라 생각된다.