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Modelling overdispersion with the normalized tempered stable distribution
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Kolossiatis, Michalis, Griffin, Jim E. and Steel, Mark F. J. (2010) Modelling overdispersion with the normalized tempered stable distribution. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Vol.2010 (No.1).

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Abstract
This paper discusses a multivariate distribution which generalizes the Dirichlet distribution
and demonstrates its usefulness for modelling overdispersion in count data. The
distribution is constructed by normalizing a vector of independent Tempered Stable random
variables. General formulae for all moments and crossmoments 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 wellstudied
BetaBinomial distribution. Examples of fitting this model to simulated and real data are
presented.
Item Type:  Working or Discussion Paper (Working Paper) 

Subjects:  Q Science > QA Mathematics 
Divisions:  Faculty of Science > Statistics 
Library of Congress Subject Headings (LCSH):  Multivariate analysis, Distribution (Probability theory) 
Series Name:  Working papers 
Publisher:  University of Warwick. Centre for Research in Statistical Methodology 
Place of Publication:  Coventry 
Official Date:  2010 
Volume:  Vol.2010 
Number:  No.1 
Number of Pages:  25 
Status:  Not Peer Reviewed 
Access rights to Published version:  Open Access 
Version or Related Resource:  Kolossiatis, M., et al. (2011). Modeling overdispersion with the normalized tempered stable distribution. Computational Statistics & Data Analysis, 55(7), pp. 22882301. http://wrap.warwick.ac.uk/id/eprint/41084 
Related URLs:  
References:  Abramowitz, M. and Stegun, I. A. (1964): “Handbook of mathematical functions with formulas, 
URI:  http://wrap.warwick.ac.uk/id/eprint/35065 
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