• Water for future
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• v.26 no.4
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• pp.73-83
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• 1993

This study focuses on the separation effect analysis of rainfall data for 2-parameter log-normal, 3-parameter log-normal, type-extreme value, 2-parameter gamma, 3-parameter gamma, log-Pearson type-III, and general extreme value distribution functions. Difference in the relationship between the mean and standard deviation of skewness for historical data and relations derived from 7 distribution functions are analyzed suing the Monte Carlo experiment. The results show that rainfall data has the separation effect for 6 distribution functions except 3-parameter gamma distribution function.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.255-266
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• 2007

A Bayesian estimation of the four-parameter gamma distribution is considered under the noninformative prior. The Bayesian estimators are obtained by the Gibbs sampling. The generation of the shape/power parameter and the power parameter in the Gibbs sampler is implemented using the adaptive rejection sampling algorithm of Gilks and Wild (1992). Also, the location parameter is generated using the adaptive rejection Metropolis sampling algorithm of Gilks, Best and Tan (1995). Finally, the simulation result is presented.

• Magazine of the Korean Society of Agricultural Engineers
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• v.31 no.4
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• pp.31-49
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• 1989

It is of the most urgent necessity to get hydrological time series of long duration for the establishment of rational design and operation criterion for the Agricultural hydraulic structures. This study was conducted to select best fitted frequency distribution for the monthly runoff and to simulate long series of generated flows by multi-season first order Markov model with comparison of statistical parameters which are derivated from observed and sy- nthetic flows in the five watersheds along Geum river basin. The results summarized through this study are as follows. 1. Both two parameter gamma and two parameter lognormal distribution were judged to be as good fitted distributions for monthly discharge by Kolmogorov-Smirnov method for goodness of fit test in all watersheds. 2. Statistical parameters were obtained from synthetic flows simulated by two parameter gamma distribution were closer to the results from observed flows than those of two para- meter lognormal distribution in all watersheds. 3. In general, fluctuation for the coefficient of variation based on two parameter gamma distribution was shown as more good agreement with the observed flow than that of two parameter lognormal distribution. Especially, coefficient of variation based on two parameter lognormal distribution was quite closer to that of observed flow during June and August in all years. 4. Monthly synthetic flows based on two parameter gamma distribution are considered to give more reasonably good results than those of two parameter lognormal distribution in the multi-season first order Markov model in all watersheds. 5. Synthetic monthly flows with 100 years for eack watershed were sjmulated by multi- season first order Markov model based on two parameter gamma distribution which is ack- nowledged to fit the actual distribution of monthly discharges of watersheds. Simulated sy- nthetic monthly flows may be considered to be contributed to the long series of discharges as an input data for the development of water resources. 6. It is to be desired that generation technique of synthetic flow in this study would be compared with other simulation techniques for the objective time series.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.861-870
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• 2005

The Bayesian model selection procedures for the shape parameter of gamma distribution are proposed in order to test that the failure rate of gamma distribution is constant, increasing or decreasing. The encompassing intrinsic Bayes factor by Beger and Pericchi (1996) based on Jeffreys prior for shape parameter is used to investigate the usefulness of the proposed Bayesian model selection procedures via both real data and pseudo data.

• 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.

• The Korean Journal of Applied Statistics
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• v.30 no.1
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• pp.95-102
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• 2017

Gamma generalized linear models have received less attention than Poisson and binomial generalized linear models. Therefore, many old-established statistical techniques are still used in gamma generalized linear models. In particular, existing literature and textbooks still use approximate estimates for the dispersion parameter. In this paper we study the efficiency of various dispersion parameter estimators in gamma generalized linear models and perform numerical simulations. Numerical studies show that the maximum likelihood estimator and Cox-Reid adjusted maximum likelihood estimator are recommended and that approximate estimates should be avoided in practice.

• Journal of Korean Society for Quality Management
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• v.22 no.1
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• pp.162-168
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• 1994

In this paper we develop an unconditional method for inferences on the shape parameter of a gamma distribution. A simple numerical implementation of this unconditional method is developed; this is a computer program that takes the observed data as input and produces the confidence distribution function for the shape parameter, which in turn provides approximate observe significance levels and confidence intervals for that parameter, as output. These approximations are extremely accurate even for very small sample size and numerically simple and easy to obtain.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.9
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• pp.1086-1093
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• 2011

To fabricate the aluminum alloys with good drawability, the textures evolution of the AA5182 sheets due to the change of lid parameter after rolling and subsequent annealing was studied. The measurement of the deformation textures was carried out for the sheets with high reduction ratio and the change of the recrystallization texture was investigated after heat-treatments of the rolled sheets in various I/d parameters. Rolling without lubrication and subsequent annealing led to the formation of favorable rot-$C_{ND}$ {001}<110> and ${\gamma}$-fiber ND//<111> textures in AA5182 sheets. From the results, the ${\gamma}$-fiber ND//<111> component well evolved during rolling at high lid parameter of 6.77. The initial shear deformation texture, especially, ${\gamma}$-fiber ND//<111> was not rotated during heat treatment in holding time of 180~7,200 seconds on AA5182 with I/d parameter of 6.77. Therefore, the AA5182 sheets were fabricated by controlling I/d parameter having well evolved ${\gamma}$-fiber ND//<111> which was advantageous in good drawability of the sheets.

• Magazine of the Korean Society of Agricultural Engineers
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• v.39 no.3
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• pp.83-95
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• 1997

This study was conducted to derive optimal design floods by Gamma distribution models of the annual maximum series at eight watersheds along Geum , Yeong San and Seom Jin river Systems, Design floods obtained by different methods for evaluation of parameters and for plotting positions in the Gamma distribution models were compared by the relative mean errors and graphical fit along with 95% confidence interval plotted on Gamma probability paper. The results were analyzed and summarized as follows. 1.Adequacy for the analysis of flood flow data used in this study was confirmed by the tests of Independence, Homogeneity and detection of Outliers. 2.Basic statistics and parameters were calculated by Gamma distribution models using Methods of Moments and Maximum Likelihood. 3.It was found that design floods derived by the method of maximum likelihood and Hazen plotting position formular of two parameter Gamma distribution are much closer to those of the observed data in comparison with those obtained by other methods for parameters and for plotting positions from the viewpoint of relative mean errors. 4.Reliability of derived design floods by both maximum likelihood and method of moments with two parameter Gamma distribution was acknowledged within 95% confidence interval.

• Journal of the Korean Data and Information Science Society
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• v.21 no.2
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.