Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

Article

Dunn, Peter K. and Smyth, Gordon K.. 2008. "Evaluation of Tweedie exponential dispersion model densities by Fourier inversion." Statistics and Computing. 18 (1), pp. 73-86. https://doi.org/10.1007/s11222-007-9039-6
Article Title

Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

ERA Journal ID861
Article CategoryArticle
AuthorsDunn, Peter K. (Author) and Smyth, Gordon K. (Author)
Journal TitleStatistics and Computing
Journal Citation18 (1), pp. 73-86
Number of Pages14
Year2008
Place of PublicationGermany
ISSN0960-3174
1573-1375
Digital Object Identifier (DOI)https://doi.org/10.1007/s11222-007-9039-6
Web Address (URL)http://springerlink.metapress.com/content/j0v757370742/?p=f1bfe0cecc6b4e33aa702fd2258f30de&pi=0
Abstract

The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V (μ) = μ^p for p not between (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.

Keywordscompound Poisson distribution; generalized linear models; numerical integration; numerical acceleration; power variance function
ANZSRC Field of Research 2020490599. Statistics not elsewhere classified
490406. Lie groups, harmonic and Fourier analysis
461399. Theory of computation not elsewhere classified
Public Notes

Deposited in accordance with the copyright policy of the publisher.
The original publication is available at www.springerlink.com

Byline AffiliationsDepartment of Mathematics and Computing
Walter and Eliza Hall Institute of Medical Research, Australia
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