Evaluation of Tweedie exponential dispersion model densities by Fourier inversion
Author(s)
Dunn, PK; Smyth, GK;
Details
Publication Year 2008-03,Volume 18,Issue #1,Page 73-86
Journal Title
STATISTICS AND COMPUTING
Publication Type
Journal Article
Abstract
The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V(mu)=mu(p) for p is not an element of (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.
Publisher
SPRINGER
Keywords
OSCILLATORY INFINITE INTEGRALS; REGRESSION-MODELS; EXTRAPOLATION; ALGORITHM
Terms of Use/Rights Notice
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Creation Date: 2008-03-01 12:00:00
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