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Modeling overdispersion with the normalized tempered stable distribution

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Author Info

  • 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.

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File URL: http://www.sciencedirect.com/science/article/B6V8V-5230PKV-2/2/72925a9ac2b75b2d761c104a79960f34
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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 55 (2011)
Issue (Month): 7 (July)
Pages: 2288-2301

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Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2288-2301

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Web page: http://www.elsevier.com/locate/csda

Related research

Keywords: Distribution on the unit simplex Mouse fetal mortality Mixed binomial Normalized random measure Overdispersion;

References

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  1. Lijoi, Antonio & Mena, Ramses H. & Prunster, Igor, 2005. "Hierarchical Mixture Modeling With Normalized Inverse-Gaussian Priors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1278-1291, December.
  2. Karen J. Palmer & Martin S. Ridout & Byron J. T. Morgan, 2008. "Modelling cell generation times by using the tempered stable distribution," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 379-397.
  3. Yu, Chang & Zelterman, Daniel, 2008. "Sums of exchangeable Bernoulli random variables for family and litter frequency data," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1636-1649, January.
  4. Steven Garren & Richard Smith & Walter Piegorsch, 2001. "Bootstrap goodness-of-fit test for the beta-binomial model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 561-571.
  5. Lancelot F. James & Antonio Lijoi & Igor Prünster, 2006. "Conjugacy as a Distinctive Feature of the Dirichlet Process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 33(1), pages 105-120.
  6. 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.
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Cited by:
  1. Stefano Favaro & Antonio Lijoi & Igor Prünster, 2012. "A new estimator of the discovery probability," DEM Working Papers Series 007, University of Pavia, Department of Economics and Management.

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