• 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.

• 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.

• 품질경영학회지
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• 제27권1호
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• pp.80-90
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• 1999

In this paper, reliability estimation using Gibbs sampler is considered for the mixture model with Gamma family, Gibbs sampler is derived to compute the features for the posterior distribution. By simulation study, the maximum likelihood estimator and the Gibbs estimator are obtained. A numerical study with a simulated data is provided.

• 응용통계연구
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• 제22권4호
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• pp.759-770
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• 2009

본 논문은 신호와 잡음이 혼합된 관측치로부터 신호 관측치를 분류하는 문제를 다룬다. 잡음은 가우시안 분포를 따르고 신호는 감마 분포를 따른다고 가정할 때 관측치의 분포는 가우시안과 감마의 혼합 분포를 따르게 된다. EM 알고리즘을 통해 혼합 모델의 모수를 추정하고 신호 및 잡음을 분류하는 것을 다중 가설 검정으로 간주하여 베이즈 오류를 바탕으로 분류를 위한 경계치를 설정한다. 제안하는 방법을 분광 데이터에 근거하여 철강 제품에서 개재물 유무를 검출하는 문제에 적용하였고 별도의 시뮬레이션 데이터를 통해 성능의 우수성을 보였다.

• Communications for Statistical Applications and Methods
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• 제9권1호
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• pp.1-11
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• 2002

This paper discusses problems of the Poisson Mixture model which Is widely used to decide the effective words in judging relevant document. Gamma Distribution model and Gauss Patterns model as an alternative of the Poisson Mixture model are studied. Classification experiments by using TREC sub-collection, WSJ[1,2] with MGQUERY and AidSearch3.0 system are discussed.

• 한국세라믹학회지
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• 제39권10호
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• pp.1007-1010
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• 2002

마이크로파 가열을 이용하여 ${\gamma}-Al_2O_3와\;Na_2SO_4$ 분말 혼합물로부터 알파 알루미나 판상체 입자를 합성하였다. 마이크로파를 이용하여 합성된 알루미나 입자의 크기와 입자분포를 마이크로파 이용 없이 동일한 혼합물로부터 합성된 분말과 비교하였다. 마이크로파를 이용하여 합성된 시료는 마이크로파 사용 없이 합성된 시료에 비하여 입자크기가 작고 입자분포가 좁음을 알 수 있었다.

• Communications for Statistical Applications and Methods
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• 제25권3호
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• pp.245-261
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• 2018

Attempts have been made to define new classes of distributions that provide more flexibility for modelling skewed data in practice. In this work we define a new extension of the generalized gamma distribution (Stacy, The Annals of Mathematical Statistics, 33, 1187-1192, 1962) for Marshall-Olkin generalized gamma (MOGG) distribution, based on the generator pioneered by Marshall and Olkin (Biometrika, 84, 641-652, 1997). This new lifetime model is very flexible including twenty one special models. The main advantage of the new family relies on the fact that practitioners will have a quite flexible distribution to fit real data from several fields, such as engineering, hydrology and survival analysis. Further, we also define a MOGG mixture model, a modification of the MOGG distribution for analyzing lifetime data in presence of cure fraction. This proposed model can be seen as a model of competing causes, where the parameter associated with the Marshall-Olkin distribution controls the activation mechanism of the latent risks (Cooner et al., Statistical Methods in Medical Research, 15, 307-324, 2006). The asymptotic properties of the maximum likelihood estimation approach of the parameters of the model are evaluated by means of simulation studies. The proposed distribution is fitted to two real data sets, one arising from measuring the strength of fibers and the other on melanoma data.

• Nuclear Engineering and Technology
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• 제56권10호
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• pp.4056-4061
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• 2024

The selection of appropriate transport parameters of radionuclides is of utmost importance in the safety assessment of radioactive waste disposal sites. Both batch and column methods are widely performed to determine the transport parameters of radionuclides through soil layers. In this paper, the distribution coefficients K_d of Co ions in sandy mixtures containing soil samples taken from Anarak near-surface repository (Iran) were determined by batch and 3 different column methods namely, breakthrough curve, thin-section, and gamma spectroscopy methods. The distribution coefficients K_d of the mixture was obtained as 160 L kg^-1 for the batch method, 23 L kg^-1, 19 L kg^-1, and 18 L kg^-1 for the breakthrough curve, the thin-section, and the gamma spectroscopy methods, respectively. These results emphasize proper selection of transport data for using in the safety assessment programs.

• Journal of the Korean Data and Information Science Society
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• 제20권5호
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• pp.933-939
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• 2009

The bivariate data in clinical research fields often has two types of failure times, which are mark variable for the first failure time and the final failure time. This paper showed how to generate bootstrap data to get Bayesian estimation for the joint distribution of bivariate survival times. The observed data was generated by Frank's family and the fake date is simulated with the Gamma prior of survival time. The bootstrap data was obtained by combining the mimic data with the observed data and the simulated fake data from the observed data.

• 응용통계연구
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• 제25권5호
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• pp.757-773
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• 2012

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.