• Title, Summary, Keyword: beta distribution

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THE BIVARIATE F3-BETA DISTRIBUTION

  • Nadarajah Saralees
    • Communications of the Korean Mathematical Society
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    • v.21 no.2
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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.

Summary on Internet Communication Network Quality Characteristics Using Beta Probability Distribution (베타 확률분포를 이용한 인터넷통신 네트워크 품질특성 요약)

  • Park Sung-Min
    • Proceedings of the Korean Operations and Management Science Society Conference
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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.

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A Note on the Beta-PERT Distribution (베타-PERT 분포에 관한 소고)

  • Bae, Bong-Soo;Seo, Sun-Keun
    • Journal of the Korea Management Engineers Society
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    • v.22 no.3
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    • pp.9-19
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    • 2017
  • Three-point time estimates in Program Evaluation and Review Technique (PERT) is widely accepted as a popular estimation method in project management and financial risk analysis because of simple structure and fairly accurate estimation. The classical PERT framework for computing mean and variance using three-point estimation formula based on beta distribution is only confined to three combinations of two beta shape parameters. Hence three beta-PERT distributions to satisfy two assumptions in three ones of PERT framework are discussed and compared in terms of flexibility of distribution, robustness, and usefulness. In this paper, new beta-PERT distribution is recommended and also demonstrated how practitioners could use this distribution in actual risk analysis of engineering projects.

On Reliability and Ratio in the Beta Case

  • Woo, Jung-Soo
    • Communications for Statistical Applications and Methods
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    • v.16 no.3
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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.

LH-Moments of Some Distributions Useful in Hydrology

  • Murshed, Md. Sharwar;Park, Byung-Jun;Jeong, Bo-Yoon;Park, Jeong-Soo
    • Communications for Statistical Applications and Methods
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    • v.16 no.4
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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.

The Minimum Dwell Time Algorithm for the Poisson Distribution and the Poisson-power Function Distribution

  • Kim, Joo-Hwan
    • Communications for Statistical Applications and Methods
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    • v.4 no.1
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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..

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Development of Precise Beta Dosimeter (사고시 대응 정밀 베타선량계 개발)

  • Lee, Won-Keun
    • Proceedings of the KIEE Conference
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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.

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Goodness of Fit and Independence Tests for Major 8 Companies of Korean Stock Market (한국 주식시장 상위 8개사에 대한 적합도 검정 및 독립성 검정)

  • Min, Seungsik
    • The Korean Journal of Applied Statistics
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    • v.28 no.6
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    • pp.1245-1255
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    • 2015
  • In this paper, we investigated the major 8 companies of Korean stock market, and carried out the goodness of fit and independence tests. We found out the distributions of absolute returns are closed to compressed exponential distribution. The parameters are dominant that 1 < ${\beta}$ < 2, followed by ${\beta}=1$(exponential distribution) and ${\beta}=2$(normal distribution). Meanwhile, we assured that most of the absolute returns for major 8 companies have relevance to each other by chi-square independence test.

CHARACTERIZATIONS OF THE PARETO DISTRIBUTION BY THE INDEPENDENCE OF RECORD VALUES

  • Chang, Se-Kyung
    • Journal of the Chungcheong Mathematical Society
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    • v.20 no.1
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    • pp.51-57
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    • 2007
  • In this paper, we establish characterizations of the Pareto distribution by the independence of record values. We prove that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}}{X_{U(n)}-X_{U(n+1)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$. And we show that $X{\in}PAR(1,{\beta})$ for ${\beta}$ > 0, if and only if $\frac{X_{U(n)}-X_{U(n+1)}}{X_{U(n)}}$ and $X_{U(n)}$ are independent for $n{\geq}1$.

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Tool condition monitoring using parameters of beta distribution in gear shaving process (기어 세이빙 공정에서 베타 확률 분포를 이용한 공구 상태 검출)

  • Choi, Deok-Ki;Kim, Seong-Jun;Oh, Young-Tak
    • Proceedings of the KSME Conference
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    • pp.1069-1074
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    • 2008
  • Tool condition monitoring (TCM) is crucial for improvement of productivity in manufacturing process. However, TCM techniques have not been applied to monitor tool failure in an industrial gear shaving application. Therefore, this work studied a statistical TCM method for monitoring gear shaving tool condition. The method modeled the shaving process using beta probability distribution in order to extract the effective features. Modeling includes rectifying for converting a bi-modal distribution into a unimodal distribution, estimating parameters of beta probability distribution based on method of moments. The usefulness of features obtained from the proposed method was evaluated and discussed.

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