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Binomial Distribution

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Gareth Hughes – One of the best experts on this subject based on the ideXlab platform.

  • bbd computer software for fitting the beta Binomial Distribution to disease incidence data
    Plant Disease, 1994
    Co-Authors: L V Madden, Gareth Hughes

    Abstract:

    A software program for DOS-based personal computers was developed to fit the beta-Binomial Distribution to the frequency of incidence of disease. The beta-Binomial is a discrete Distribution, which is appropriate for describing aggregated or clustered binary data such as incidence. Variance-ratio and C(α) tests are performed to determine if there is evidence that incidence is aggregated. The program then calculates Distribution parameters and their standard errors using a maximum likelihood procedure, determines the expected values of the Distribution, and calculates a chi-square goodness-of-fit test. For comparison purposes, the program fits the Binomial Distribution to the same data. The software and a detailed user’s manual are available free from either author

  • using the beta Binomial Distribution to describe aggregated patterns of disease incidence
    Phytopathology, 1993
    Co-Authors: Gareth Hughes, L V Madden

    Abstract:

    We discuss the use of the beta-Binomial Distribution for the description of plant disease incidence data, collected on the basis of scoring plants as either «diseased» or «healthy». The beta-Binomial is a discrete probability Distribution derived by regarding the probability of a plant being diseased (a constant in the Binomial Distribution) as a beta-distributed variable. An important characteristic of the beta-Binomial is that its variance is larger than that of the Binomial Distribution with the same mean. The beta-Binomial Distribution, therefore, may serve to describe aggregated disease incidence data. Using maximum likelihood, we estimated beta-Binomial parameters p (mean disease incidence) and θ (an index of aggregation) for four previously published sets of disease incidence data in which there were some indications of aggregation […]

L V Madden – One of the best experts on this subject based on the ideXlab platform.

  • bbd computer software for fitting the beta Binomial Distribution to disease incidence data
    Plant Disease, 1994
    Co-Authors: L V Madden, Gareth Hughes

    Abstract:

    A software program for DOS-based personal computers was developed to fit the beta-Binomial Distribution to the frequency of incidence of disease. The beta-Binomial is a discrete Distribution, which is appropriate for describing aggregated or clustered binary data such as incidence. Variance-ratio and C(α) tests are performed to determine if there is evidence that incidence is aggregated. The program then calculates Distribution parameters and their standard errors using a maximum likelihood procedure, determines the expected values of the Distribution, and calculates a chi-square goodness-of-fit test. For comparison purposes, the program fits the Binomial Distribution to the same data. The software and a detailed user’s manual are available free from either author

  • using the beta Binomial Distribution to describe aggregated patterns of disease incidence
    Phytopathology, 1993
    Co-Authors: Gareth Hughes, L V Madden

    Abstract:

    We discuss the use of the beta-Binomial Distribution for the description of plant disease incidence data, collected on the basis of scoring plants as either «diseased» or «healthy». The beta-Binomial is a discrete probability Distribution derived by regarding the probability of a plant being diseased (a constant in the Binomial Distribution) as a beta-distributed variable. An important characteristic of the beta-Binomial is that its variance is larger than that of the Binomial Distribution with the same mean. The beta-Binomial Distribution, therefore, may serve to describe aggregated disease incidence data. Using maximum likelihood, we estimated beta-Binomial parameters p (mean disease incidence) and θ (an index of aggregation) for four previously published sets of disease incidence data in which there were some indications of aggregation […]

Ming Han – One of the best experts on this subject based on the ideXlab platform.

  • the m bayesian credible limits of the reliability derived from Binomial Distribution
    Communications in Statistics-theory and Methods, 2012
    Co-Authors: Ming Han

    Abstract:

    This article introduces a new method, M-Bayesian credible limit method, to estimate reliability derived from Binomial Distribution, in the case of zero-failure data. Firstly, the definition of one-sided and two-sided M-Bayesian credible limits are provided, and moreover, formulas of one-sided and two-sided M-Bayesian credible limits are also provided. secondly, properties of one-sided and two-sided M-Bayesian credible limits are discussed, and we will see that the M-Bayesian credible limit method is superior to the corresponding classical confidence limit method. Finally, the new estimation method is applied to a numerical example. Through the example the efficiency and easiness of operation of this method are commended.

  • e bayesian estimation of the reliability derived from Binomial Distribution
    Applied Mathematical Modelling, 2011
    Co-Authors: Ming Han

    Abstract:

    This paper introduces a new parameter estimation method, named E-Bayesian estimation method, to estimate reliability derived from Binomial Distribution. The definition of E-Bayesian estimation of the reliability is proposed, the formulas of E-Bayesian estimation and hierarchical Bayesian estimation of the reliability are also provided. Finally, it is shown, through a numerical example, that the new method is much simpler than hierarchical Bayesian estimation in practice.