• Communications for Statistical Applications and Methods
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• 제31권3호
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• pp.263-277
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• 2024

This paper proposes new parameterizations of the tilted beta binomial distribution, obtained from the combination of the binomial distribution and the tilted beta distribution, where the beta component of the mixture is parameterized as a function of their mean and variance. These new parameterized distributions include as particular cases the beta rectangular binomial and the beta binomial distributions. After that, we propose new linear regression models to deal with overdispersed binomial datasets. These new models are defined from the proposed new parameterization of the tilted beta binomial distribution, and assume regression structures for the mean and variance parameters. These new linear regression models are fitted by applying Bayesian methods and using the OpenBUGS software. The proposed regression models are fitted to a school absenteeism dataset and to the seeds germination rate according to the type seed and root.

• Nuclear Engineering and Technology
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• 제54권10호
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• pp.3811-3815
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• 2022

Ni-63 is pure beta source which emits low energy beta particles. The Ni-63 sources were fabricated to develop the beta-voltaic battery which converts decay energy into electrical energy for power generation. Activity distribution of the source was important factor of power producibility of the beta-voltaic battery. Liquid scintillation counter widely used for measurement of low energy beta emitters was not suitable to measure activity distribution. In this study, we used the peeled-off Gafchromic™ EBT3 film to measure the activity distribution of the Ni-63 source. Absorbed dose was increased proportionally to the source activity and exposure duration. The low energy beta particles could transport the energy into the active layer without the polyester protective layer. Also, Activity distribution was measured by using the peeled-off EBT3 film. Two-dimensional dosimetric distribution was suitable to measure the activity distribution. To use the peeled-off EBT3 film is user-friendly and cost-effective method for quality assurance of the Ni-63 sources for the beta-voltaic battery.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 2006년도 춘계공동학술대회 논문집
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• pp.1661-1662
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• 2006

Internet communication network quality characteristics are analyzed using Beta probability distribution. Beta probability distribution is chosen for the underlying probability distribution because it is an extremely flexible probability distribution used to model bounded random variables. Based on the fitted Beta probability distribution, a dataset regarding each network quality characteristic is summarized concisely.

• 대한수학회논문집
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• 제21권2호
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• pp.363-374
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• 2006

A new bivariate beta distribution based on the Appell function of the third kind is introduced. Various representations are derived for its product moments, marginal densities, marginal moments, conditional densities and conditional moments. The method of maximum likelihood is used to derive the associated estimation procedure as well as the Fisher information matrix.

• 호남수학학술지
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• 제46권2호
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• Communications for Statistical Applications and Methods
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• 제16권4호
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• pp.647-658
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• 2009

It is already known from the previous study that flood seems to have heavier tail. Therefore, to make prediction of future extreme label, some agreement of tail behavior of extreme data is highly required. The LH-moments estimation method, the generalized form of L-moments is an useful method of characterizing the upper part of the distribution. LH-moments are based on linear combination of higher order statistics. In this study, we have formulated LH-moments of five distributions useful in hydrology such as, two types of three parameter kappa distributions, beta-${\kappa}$ distribution, beta-p distribution and a generalized Gumbel distribution. Using LH-moments reduces the undue influences that small sample may have on the estimation of large return period events.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 추계학술대회 논문집 학회본부
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• pp.468-470
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• 1996

The use of thermoluminescent dosimeters (TLDs) for beta dosimetry has been encumbered by the energy-dependent responses of TLDs to beta radiation. This energy-dependent response is due to the low penetrating ability of beta particles. Thus the determination of the beta dose imparted to an exposed TLD chip can be accurately determined only if the energy distribution of beta radiation is correctly accounted for. So precise beta dosimeter used TLD chips place under several aluminum filters of varying thicknesses and developed to correctly determine doses due to radiation fields where the beta energy distribution is unknown.

• Communications for Statistical Applications and Methods
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• 제4권1호
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• pp.229-241
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• 1997

We consider discrimination curve and minimum dwell time for Poisson distribution and Poisson-power function distribution. Let the random variable X has Poisson distribution with mean .lambda.. For the hypothesis testing H$\_$0/:.lambda. = t vs. H$\_$1/:.lambda. = d (d$\_$0/ if X.leq.c. Since a critical value c can not be determined to satisfy both types of errors .alpha. and .beta., we considered discrimination curve that gives the maximum d such that it can be discriminated from t for a given .alpha. and .beta.. We also considered an algorithm to compute the minimum dwell time which is needed to discriminate at the given .alpha. and .beta. for the Poisson counts and proved its convergence property. For the Poisson-power function distribution, we reject H$\_$0/ if X.leq..'{c}.. Since a critical value .'{c}. can not be determined to satisfy both .alpha. and .beta., similar to the Poisson case we considered discrimination curve and computation algorithm to find the minimum dwell time for the Poisson-power function distribution. We prosent this algorithm and an example of computation. It is found that the minimum dwell time algorithm fails for the Poisson-power function distribution if the aiming error variance .sigma.$\^$2/$\_$2/ is too large relative to the variance .sigma.$\^$2/$\_$1/ of the Gaussian distribution of intensity. In other words, if .ell. is too small, we can not find the minimum dwell time for a given .alpha. and .beta..

• 응용통계연구
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• 제28권6호
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• pp.1245-1255
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• 2015

본 논문에서는 한국 유가증권시장의 시가총액 상위 8개사 주가 수익률 절대값(absolute return)을 이용하여, 분포의 적합도 검정(goodness of fit test) 및 기업들 간의 독립성 검정(independence test)을 실시하였다. 검정 결과 개별 주가 수익률은 압축된 지수분포(compressed exponential distribution)를 이루는 것으로 나타났다. 이 때 파라미터는 1 < ${\beta}$ < 2 인 경우가 ${\beta}=1$(지수분포), ${\beta}=2$(정규분포)보다 우세한 것으로 확인되었다. 한편 독립성 검정에서는 대부분의 기업들이 관련성을 지니고 있는 것으로 나타났다.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.