• Journal of the Korean Statistical Society
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• v.34 no.1
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• pp.35-38
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• 2005

A single, tractable, special case of the problem of continuous mixtures of beta distributions over their parameters is considered. This is the uniform mixture of generalized arc-sine distributions which, curiously, turns out to be linked by transformation to the Cauchy distribution.

• Proceedings of the Korea Water Resources Association Conference
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• 1992.07a
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• pp.55-66
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• 1992

The energy and momentum coefficients ${\alpha}$ and ${\beta}$ are measures of homogenerity of velocity distribution in a chanel section. They indicate the effect of energy and momentum transport. However, in most practical applications, they are assumed to be unity due to the difficulty in estimating them. Efforts have been made in this study to estimate these coefficients and to develop equations for practical applications. The Prandtl-von Karman logarithmic equation as being used today has limitations and far-reaching assumptions. Therefore, this paper uses Chiu's velocity distribution equation which seems to be capable of serving as such an alternative, to estimate the velocity distribution and the energy and momentum coefficients, ${\alpha}$ and ${\beta}$ results are compared with those computed by other existing equations. For practical applications, this paper also uses Chiu's equation along with the Mannig's equation to calculate ${\alpha}$, ${\beta}$ without velocity data

• Journal of the Korean Applied Science and Technology
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• v.16 no.2
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• pp.117-125
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• 1999

The alkylation benzene with 1-dodecene of Mordenite, Zeolite ${\beta}$ and Zeolite Y was studied in the stirring batch reactor. The kinds of zeolites were found to have influenced the reaction conversion and distribution of phenyldodecane isomer in the product. Compared to the alkylation conducted over Zeolite Y and Zeolite ${\beta}$, the alkylation over Mordenite exhibited higher distribution of 2-phenyldodecane and the alkylation conducted over Zeolite Y and Mordenite, the alkylation over Zeolite ${\beta}$ exhibited higher distribution of heavy alkylate which formed through oligomerization reaction readily deactivated the Lewis acid sites. A special feature of the effect of the benzene to 1-dodecene ratio the reaction conversion and selectivity of phenyldodecane isomer was found. At alkylation of benzene with 1-dodecene over Zeolite ${\beta}$, when the catalyst content in the system was high, the reaction will reach the optimal conversion at the higher B/D. When the benzene to 1-dodecene ratio was high, the selectivity of phenyldodecane isomer is high. It was also found that at the similar reaction conversion there was the same product distribution regardless of D/C ratio.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.481-498
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• 2001

Empirical Bayes procedure of nonparametric estiamtion of cumulative hazard rates based on censored data is considered using the beta process priors of Hjort(1990). Beta process priors with unknown parameters are used for cumulative hazard rates. Empirical Bayes estimators are suggested and asymptotic optimality is proved. Our result generalizes that of Susarla and Van Ryzin(1978) in the sensor that (i) the cumulative hazard rate induced by a Dirichlet process is a beta process, (ii) our empirical Bayes estimator does not depend on the censoring distribution while that of Susarla and Van Ryzin(1978) does, (iii) a class of estimators of the hyperprameters is suggested in the prior distribution which is assumed known in advance in Susarla and Van Ryzin(1978). This extension makes the proposed empirical Bayes procedure more applicable to real dta sets.

• Communications for Statistical Applications and Methods
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• v.11 no.3
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• pp.619-629
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• 2004

Binomial group testing or composite sampling is often used to estimate the proportion, p, of positive(infects, defectives) in a population when that proportion is known to be small; the potential benefits of group testing over one-at-a-time testing are well documented. The literature has focused on maximum likelihood estimation. We provide two Bayes estimators and compare them with the MLE. The first of our Bayes estimators uses an uninformative Uniform (0, 1) prior on p; the properties of this estimator are poor. Our second Bayes estimator uses a much more informative prior that recognizes and takes into account key aspects of the group testing context. This estimator compares very favorably with the MSE, having substantially lower mean squared errors in all of the wide range of cases we considered. The priors uses a Beta distribution, Beta ($\alpha$, $\beta$), and some advice is provided for choosing the parameter a and $\beta$ for that distribution.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.8
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• pp.854-867
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• 2014

This paper deals with the performance comparison of a PSO algorithm inspired in the process of simulating the behavior pattern of the organisms. The PSO algorithm finds the optimal solution (fitness value) of the objective function based on a stochastic process. Generally, the stochastic process, a random function, is used with the expression related to the velocity included in the PSO algorithm. In this case, the random function of the normal distribution (Gaussian) or uniform distribution are mainly used as the random function in a PSO algorithm. However, in this paper, because the probability distribution which is various with 2 shape parameters can be expressed, the performance comparison of a PSO algorithm using the beta probability distribution function, that is a random function which has a high degree of freedom, is introduced. For performance comparison, 3 functions (Rastrigin, Rosenbrock, Schwefel) were selected among the benchmark Set. And the convergence property was compared and analyzed using PSO-FIW to find the optimal solution.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.15-27
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• 2018

Parametric method of flood frequency analysis involves fitting of a probability distribution to observed flood data. When record length at a given site is relatively shorter and hard to apply the asymptotic theory, an alternative distribution to the generalized extreme value (GEV) distribution is often used. In this study, we consider the beta-P distribution (BPD) as an alternative to the GEV and other well-known distributions for modeling extreme events of small or moderate samples as well as highly skewed or heavy tailed data. The L-moments ratio diagram shows that special cases of the BPD include the generalized logistic, three-parameter log-normal, and GEV distributions. To estimate the parameters in the distribution, the method of moments, L-moments, and maximum likelihood estimation methods are considered. A Monte-Carlo study is then conducted to compare these three estimation methods. Our result suggests that the L-moments estimator works better than the other estimators for this model of small or moderate samples. Two applications to the annual maximum stream flow of Colorado and the rainfall data from cloud seeding experiments in Southern Florida are reported to show the usefulness of the BPD for modeling hydrologic events. In these examples, BPD turns out to work better than $beta-{\kappa}$, Gumbel, and GEV distributions.

• Journal of Environmental Science International
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• v.26 no.11
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• pp.1247-1253
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• 2017

The Fuji variety of apple, introduced in Japan, has excellent storage quality and good taste, such that it is the most commonly cultivated apple variety in Gunwi County, North Gyeongsang Province, Korean Peninsula. Accurate prediction of harvest maturity allows farmers to more efficiently manage their farm in important aspects such as working time, fruit storage, market shipment, and labor distribution. Temperature is one of the most important factors that determine plant growth, development, and yield. This paper reports on the beta distribution (function) model that can be used to simulate the the phenological response of plants to temperature. The beta function, commonly used as a skewed probability density in statistics, was introduced to estimate apple harvest maturity as a function of temperature in this study. The model parameters were daily maximum temperature, daily optimum temperature, and maximum growth rate. They were estimated from the input data of daily maximum and minimum temperature and apple harvest maturity. The difference in observed and predicted maturity day from 2009 to 2012, with optimal parameters, was from two days earlier to one day later.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.81-86
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• 1994

A Chi-square approximation to the distribution of product of independent Beta variates denoted by U is developed. The distribution is commonly used as a test criterion for the general linear hypothesis about the multivariate linear models. The approximation is obtained by fitting a logarithmic function of U to a Chi-square variate in terms of the first three moments. It is compared with the well known approximations due to Box(1949), Rao(1948), and Mudholkar and Trivedi(1980). It is found that the Chi-square approximation compares favorably with the other three approximations.

• Food Science and Biotechnology
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• v.15 no.1
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• pp.96-101
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• 2006

Isoflavone distribution and ${\beta}$-glucosidase activity in cheonggukjang, a traditional Korean whole soybean-fermented food prepared with or without addition of Bacillus subtilis, were analyzed every 6 hr for 36 hr. Thermal cooking of raw-soaked soybeans significantly increased ${\beta}$-glucoside isoflavone level by 57.1 % and decreased malonyl-${\beta}$-glucosides by 57.6% (p<0.05). Consistent changes of isoflavone profiles in cheonggukjang without B. subtilis addition (COB) and samples with addition of B. subtilis (CWB) were not observed during 36 hr fermentation. ${\beta}$-Glucosides of isoflavones are major forms in both COB and CWB. ${\beta}$-Glucosidase activity in cheonggukjang decreased significantly compared to that of soaked soybeans due to thermal denaturation, while recovery of enzyme activity in COB was observed. Two new unidentified peaks were detected, and their relative peak areas in CWB were significantly larger than those in COB with increasing fermentation period (p<0.05), which indicates both peaks could be associated with fermentation metabolites.