# 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 861 Article Dunn, Peter K. (Author) and Smyth, Gordon K. (Author) Statistics and Computing 18 (1), pp. 73-86 14 2008 Germany 0960-3174 1573-1375 https://doi.org/10.1007/s11222-007-9039-6 http://springerlink.metapress.com/content/j0v757370742/?p=f1bfe0cecc6b4e33aa702fd2258f30de&pi=0 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 parameterspace. compound Poisson distribution; generalized linear models; numerical integration; numerical acceleration; power variance function 490599. Statistics not elsewhere classified 490406. Lie groups, harmonic and Fourier analysis 461399. Theory of computation not elsewhere classified Deposited in accordance with the copyright policy of the publisher.The original publication is available at www.springerlink.com Department of Mathematics and Computing Walter and Eliza Hall Institute of Medical Research, Australia

https://research.usq.edu.au/item/9y99q/evaluation-of-tweedie-exponential-dispersion-model-densities-by-fourier-inversion

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