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Modeling overdispersion with the normalized tempered stable distribution

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  • Kolossiatis, M.
  • Griffin, J.E.
  • Steel, M.F.J.

Abstract

A multivariate distribution which generalizes the Dirichlet distribution is introduced and its use for modeling overdispersion in count data is discussed. The distribution is constructed by normalizing a vector of independent tempered stable random variables. General formulae for all moments and cross-moments of the distribution are derived and they are found to have similar forms to those for the Dirichlet distribution. The univariate version of the distribution can be used as a mixing distribution for the success probability of a binomial distribution to define an alternative to the well-studied beta-binomial distribution. Examples of fitting this model to simulated and real data are presented.

Suggested Citation

  • Kolossiatis, M. & Griffin, J.E. & Steel, M.F.J., 2011. "Modeling overdispersion with the normalized tempered stable distribution," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2288-2301, July.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2288-2301
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    References listed on IDEAS

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    7. Antonio Lijoi & Ramsés H. Mena & Igor Prünster, 2007. "Controlling the reinforcement in Bayesian non‐parametric mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 715-740, September.
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    9. Zhen Pang & Anthony Y. C. Kuk, 2005. "A Shared Response Model for Clustered Binary Data in Developmental Toxicity Studies," Biometrics, The International Biometric Society, vol. 61(4), pages 1076-1084, December.
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