Evaluation of Tweedie exponential dispersion model densities by Fourier inversion

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. ISSN 0960-3174

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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.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Deposited in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com
Depositing User: Dr Peter Dunn
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 26 Feb 2008 04:30
Last Modified: 02 Jul 2013 22:58
Uncontrolled Keywords: compound Poisson distribution; generalized linear models; numerical integration; numerical acceleration; power variance function
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0101 Pure Mathematics > 010106 Lie Groups, Harmonic and Fourier Analysis
08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080205 Numerical Computation
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1007/s11222-007-9039-6
URI: http://eprints.usq.edu.au/id/eprint/3888

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