Journal article
Evaluation of Tweedie exponential dispersion model densities by Fourier inversion
Statistics and Computing, Vol.18(1), pp.73-86
2008
Abstract
The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V(μ)=μ p for . 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.
Details
- Title
- Evaluation of Tweedie exponential dispersion model densities by Fourier inversion
- Authors
- Peter K Dunn (Author) - University of Southern QueenslandG K Smyth (Author) - Walter and Eliza Hall Institute of Medical Research
- Publication details
- Statistics and Computing, Vol.18(1), pp.73-86
- Publisher
- Springer New York LLC
- Date published
- 2008
- DOI
- 10.1007/s11222-007-9039-6
- ISSN
- 0960-3174
- Copyright note
- Copyright © 2008 Springer New York LLC. The author's accepted version is reproduced here in accordance with the publisher's copyright policy. The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-007-9039-6
- Organisation Unit
- University of the Sunshine Coast, Queensland; School of Health and Sport Sciences - Legacy; School of Science, Technology and Engineering
- Language
- English
- Record Identifier
- 99449898302621
- Output Type
- Journal article
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