Statistics and Computing

, Volume 18, Issue 1, pp 73–86 | Cite as

Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

  • Peter K. DunnEmail author
  • Gordon K. Smyth


The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V(μ)=μ p for \(p\not\in(0,1)\) . These distributions do not generally have density functions that can be written in closed form. However, they have simple moment generating functions, so the densities can be evaluated numerically by Fourier inversion of the characteristic functions. This paper develops numerical methods to make this inversion fast and accurate. Acceleration techniques are used to handle oscillating integrands. A range of analytic results are used to ensure convergent computations and to reduce the complexity of the parameter space. The Fourier inversion method is compared to a series evaluation method and the two methods are found to be complementary in that they perform well in different regions of the parameter space.


Compound Poisson distribution Generalized linear models Numerical integration Numerical acceleration Power variance function 


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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Australian Centre for Sustainable Catchments and Department of Mathematics and ComputingUniversity of Southern QueenslandToowoombaAustralia
  2. 2.Bioinformatics DivisionWalter and Eliza Hall Institute of Medical ResearchMelbourneAustralia

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