Generation of Over-Dispersed and Under-Dispersed Binomial Variates

Ahn, Hongshik; Chen, James J.

doi:10.1080/10618600.1995.10474665

Cited by 16 publications

(15 citation statements)

References 10 publications

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“…In such a case, it is known that the sumX i of N dependent Bernouilli trials can be modelled with a beta-binomial distribution, see e.g. Ahn and Chen (1995) or Tsai, et al (2003). This distribution is defined asX Note that, for the sake of simplicity, the beta distribution Beta(α i , σ θ ) in the above is characterized by its mean α i and variance σ θ , instead of its two shape parameters.…”

Section: Discussionmentioning

confidence: 99%

Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation

Pinson

McSharry

Madsen

2010

Quart J Royal Meteoro Soc

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Reliability is seen as a primary requirement when verifying probabilistic forecasts, since a lack of reliability would introduce a systematic bias in subsequent decisionmaking. Reliability diagrams comprise popular and practical diagnostic tools for the reliability evaluation of density forecasts of continuous variables. Such diagrams relate to the assessment of the unconditional calibration of probabilistic forecasts. A reason for their appeal is that deviations from perfect reliability can be visually assessed based on deviations from the diagonal. Deviations from the diagonal may, however, be caused by both sampling effects and serial correlation in the forecastverification pairs. We build on a recent proposal, consisting of associating reliability diagrams with consistency bars that would reflect the deviations from the diagonal that are potentially observable even if density forecasts are perfectly reliable. Our consistency bars, however, reflect potential deviations originating from the combined effects of limited counting statistics and serial correlation in the forecastverification pairs. They are generated based on an original surrogate consistency resampling method. Its ability to provide consistency bars with a significantly better coverage against the independent and identically distributed (i.i.d.) resampling alternative is shown from simulations. Finally, a practical example of the reliability assessment of non-parametric density forecasts of short-term wind-power generation is given.

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Section: Discussionmentioning

confidence: 99%

Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation

Pinson

McSharry

Madsen

2010

Quart J Royal Meteoro Soc

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“…Initially, we tried to use the drnbet fortran IMSL subroutine to generate the DM distributions and we saw that it does not generate observations correctly from the beta distribution. Later, we discovered that Ahn and James (1995) had the same problem, and for this reason we have used the G05FEF fortran NAG subroutine.…”

Section: Simulation Studymentioning

confidence: 99%

“…Ahn and James (1995) presented an algorithm for generating overdispersed binomial distributions. Some examples of distributions for Y ( ) , with expectation vector and variancecovariance given in (1.8), are the following: the Dirichletmultinomial, the random-clumped multinomial and n-inflated multinomial distributions.…”

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confidence: 99%

New improved estimators for overdispersion in models with clustered multinomial data and unequal cluster sizes

Alonso-Revenga

Martín

2015

Stat Comput

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It is usual to rely on the quasi-likelihood methods for deriving statistical methods applied to clustered multinomial data with no underlying distribution. Even though extensive literature can be encountered for these kind of data sets, there are few investigations to deal with unequal cluster sizes. This paper aims to contribute to fill this gap by proposing new estimators for the intracluster correlation coefficient.

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“…However, since our present study focuses on comparing three Binomial mixture distributions including the Beta-Binomial distribution in handling overdispersed Binomial data, there is a suspicion that perhaps the results may be influenced towards Beta-Binomial distribution. Therefore an alternative algorithm proposed by Ahn and Chen (1995) is used to simulate overdispersed Binomial variables. The algorithm developed by Ahn and Chen (1995) to generate overdispersed Binomial variables for specified mean and variance from an underlying multivariate normal distribution is simplified using equal correlation structure and briefly outlined in subsection 7.1.1.…”

Section: Generation Of Overdispersed Binomial Variatesmentioning

confidence: 99%

“…Therefore an alternative algorithm proposed by Ahn and Chen (1995) is used to simulate overdispersed Binomial variables. The algorithm developed by Ahn and Chen (1995) to generate overdispersed Binomial variables for specified mean and variance from an underlying multivariate normal distribution is simplified using equal correlation structure and briefly outlined in subsection 7.1.1.…”

Section: Generation Of Overdispersed Binomial Variatesmentioning

confidence: 99%

The McDonald Generalized Beta-Binomial Distribution: A New Binomial Mixture Distribution and Simulation Based Comparison with Its Nested Distributions in Handling Overdispersion

Chandrabose¹,

Wijekoon²,

Yapa³

2013

IJSP

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The binomial outcome data are widely encountered in many real world applications. The Binomial distribution often fails to model the binomial outcomes since the variance of the observed binomial outcome data exceeds the nominal Binomial distribution variance, a phenomenon known as overdispersion. One way of handling overdispersion is modeling the success probability of the Binomial distribution using a continuous distribution defined on the standard unit interval. The resultant general class of univariate discrete distributions is known as the class of Binomial mixture distributions. The Beta-Binomial (BB) distribution is a prominent member of this class of distributions. The Kumaraswamy-Binomial (KB) distribution is another recent member of this class. In this paper we focus the emphasis on the McDonald's Generalized Beta distribution of the first kind as the mixing distribution and introduce a new Binomial mixture distribution called the McDonald Generalized Beta-Binomial distribution(McGBB). Some theoretical properties of McGBB are discussed. The parameters of the McGBB distribution are estimated via maximum likelihood estimation technique. A real world dataset is modeled by using the new McGBB mixture distribution, and it is shown that this model gives better fit than its nested models. Finally, an extended simulation study is presented to compare the McGBB distribution with its nested distributions in handling overdispersed binomial outcome data.

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Generation of Over-Dispersed and Under-Dispersed Binomial Variates

Cited by 16 publications

References 10 publications

Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation

Reliability diagrams for non‐parametric density forecasts of continuous variables: Accounting for serial correlation

New improved estimators for overdispersion in models with clustered multinomial data and unequal cluster sizes

The McDonald Generalized Beta-Binomial Distribution: A New Binomial Mixture Distribution and Simulation Based Comparison with Its Nested Distributions in Handling Overdispersion

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