• 대한수학회보
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• 제55권5호
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• pp.1563-1575
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• 2018

In this paper, our central focus is upon gamma and beta q-distributions from a probabilistic viewpoint. The gamma and the beta q-distributions are characterized by investing the nature of the joint q-probability density function through the q-independence property and the q-Laplace transform.

• Communications for Statistical Applications and Methods
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• 제24권2호
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• pp.129-142
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• 2017

In this paper we consider the problem of the model selection/discrimination among three different positively skewed lifetime distributions. Lindley, Weibull, and gamma distributions have been used to effectively analyze positively skewed lifetime data. This paper assesses how much closer the Lindley distribution gets to Weibull and gamma distributions. We consider three techniques that involve the likelihood ratio test, asymptotic likelihood ratio test, and minimum Kolmogorov distance as optimality criteria to diagnose the appropriate fitting model among the three distributions for a given data set. Monte Carlo simulation study is performed for computing the probability of correct selection based on the considered optimality criteria among these families of distributions for various choices of sample sizes and shape parameters. It is observed that overall, the Lindley distribution is closer to Weibull distribution in the sense of likelihood ratio and Kolmogorov criteria. A real data set is presented and analyzed for illustrative purposes.

• 한국농공학회논문집
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• 제46권4호
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• pp.25-36
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• 2004

This study was conducted to derive the design rainfall by the consecutive duration using the at-site frequency analysis. Using the errors, K-S tests and LH-moment ratios, Log Pearson type 3 (LP3) and Generalized Extreme Value (GEV) distributions of Gamma and Non-Gamma Family, respectively were identified as the optimal probability distributions among applied distributions. Parameters of GEV and LP3 distributions were estimated by the method of L and LH-moments and the Indirect method of moments respectively. Design rainfalls following the consecutive duration were derived by at-site frequency analysis using the observed and simulated data resulted from Monte Carlo techniques. Relative root-mean-square error (RRMSE) and relative efficiency (RE) in RRMSE for the design rainfall derived by at-site analysis in the observed and simulated data were computed and compared. It has shown that at-site frequency analysis by GEV distribution using L-moments is confirmed as more reliable than that of GEV and LP3 distributions using LH-moments and Indirect method of moments in view of relative efficiency.

• 한국농공학회:학술대회논문집
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• 한국농공학회 2003년도 학술발표논문집
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• pp.439-442
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• 2003

This study was conducted to choose optimal distribution and to estimate properly parameters for the derivation of design rainfall in Gamma Family. Design rainfall derived by Gamma Family Distributions were compared by the Relative Mean Errors(RME) and Relative Absolute Errors(RAE) for the consecutive durations of 1, 3, 6, 12, 24, 36, 48 and 72hr and 65 regions all over the regions except Cheju and Wulreung islands in Korea. Consequently, Design rainfall derived by Indirect Method of Moments in the Log-Pearson Type 3 distribution are seemed to be more reasonable than those of other distributions in Gamma Family.

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.221-230
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• 2007

The exponential and the gamma distributions have been the traditional models for drought duration and drought intensity data, respectively. However, it is often assumed that the drought duration and drought intensity are independent, which is not true in practice. In this paper, an application of the bivariate gamma exponential distribution is provided to drought data from Nebraska. The exact distributions of R=X+Y, P=XY and W=X/(X+Y) and the corresponding moment properties are derived when X and Y follow this bivariate distribution.

• International Journal of Reliability and Applications
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• 제15권2호
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• pp.111-123
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• 2014

A new class of bivariate distributions is derived by specifying its conditionals as the exponential and gamma distributions. Some properties and relations with other distributions of the new class are studied. In particular, the estimation of parameters is considered by the methods of maximum likelihood and pseudolikelihood of a special case of the new class. An application using a real bivariate data is given for illustrating the flexibility of the new class in this context, and, also, for comparing the estimation results obtained by the maximum likelihood and pseudolikelihood methods.

• Korea-Australia Rheology Journal
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• 제17권3호
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• pp.125-130
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• 2005

Coalescence process of binary immiscible fluid mixtures having bimodal size distributions, prepared by mixing two pre-sheared samples at different shear rates, ${\gamma}_{pre1}\;and\;{\gamma}_{pre2}$, under shear flow at a final shear rate, ${\gamma}_f$, are examined by transient shear stress measurements and microscopic observations in comparison with the results for simply pre-sheared samples having narrow size distributions (unimodal distribution samples). Component fluids are a silicone oil (PDMS) and a hydrocarbon-formaldehyde resin (Genelite) and their viscosities are 14.1 and 21.0 $pa{\cdot}sec$ at room temperature $(ca.\;20^{\circ}C)$, respectively. The weight ratio of PDMS: Genelite was 7:3. Three cases, $({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;({\gamma}_{pre1}=0.8sec^{-1},\;{\gamma}_{pre2}=4.0sec^{-1}\;and\;{\gamma}_f=2.4sec^{-1}),\;and\;({\gamma}_{pre1}=7.2sec^{-1},\;{\gamma}_{pre2}=12.0^sec^{-1}\;and\;{\gamma}_f=7.2sec^{-1})$ the first case, transient shear stress did not show any significant difference but domains larger than the initial state are observed at short times. In the latter cases, there exist undershoot of shear stress, reflecting existence of deformed large domains, which is confirmed by the direct observation. It is concluded that coalescence between large and small domains more frequently occur than coalescence between the domains with similar size in the bimodal distribution samples.

• Journal of Radiation Protection and Research
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• 제44권1호
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• pp.1-7
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• 2019

Background: To monitor proton beam in proton therapy, prompt gamma imaging systems are being developed by several research groups, and these systems are expected to improve the quality of the treatment and the patient safety. To apply the prompt gamma imaging systems into spot scanning proton therapy, the systems should be able to monitor the proton beam range of a spot with a small number of protons ( <$10^8$ protons), which is quite often not the case due to insufficient prompt gamma statistics. Materials and Methods: In the present study, we propose to improve prompt gamma statistics by merging the prompt gamma distributions of several individual spots into a new distribution. This proposal was tested by Geant4 Monte Carlo simulations for a multi-slit prompt gamma camera which has been developed to measure the proton beam range in the patient. Results and Discussion: The results show that the proposed method clearly enhance the statistical precision of beam range measurement. The accuracy of beam range verification is improved, within ~1.4 mm error, which is not achievable before applying the developed method. Conclusion: In this study, we tried to improve the statistics of the prompt gamma statistics by merging the prompt gamma distributions of multiple spots, and it was found that the merged distribution provided sufficient prompt gamma statistics and the proton beam range was determined accurately.

• Journal of Microbiology and Biotechnology
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• 제27권2호
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• pp.412-415
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• 2017

Prebiotics improve the growth or activities of specific microbial genera and species in the gut microbiota in order to confer health benefits to the host. In this study, we investigated the effect of poly-gamma-glutamate (${\gamma}-PGA$) as a prebiotic on the gut microbiota of mice and the organ distributions of ${\gamma}-PGA$ in mice. Pyrosequencing analysis for 16S rRNA genes of bacteria indicated that oral administration of ${\gamma}-PGA$ increased the abundance of Lactobacillales while reducing the abundance of Clostridiales in murine guts. It is suggested that oral administration of ${\gamma}-PGA$ can be helpful for modulating the gut microbiota as a prebiotic.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.27-34
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• 2005

We consider the problem of estimating the system reliability noninformative priors when both stress and strength follow generalized gamma distributions. We first derive Jeffreys' prior, group ordering reference priors, and matching priors. We investigate the propriety of posterior distributions and provide marginal posterior distributions under those noninformative priors. We also examine whether the reference priors satisfy the probability matching criterion.