Evaluation of Tweedie exponential dispersion model densities by Fourier inversion
Article
Article Title | Evaluation of Tweedie exponential dispersion model densities by Fourier inversion |
---|---|
ERA Journal ID | 861 |
Article Category | Article |
Authors | Dunn, Peter K. (Author) and Smyth, Gordon K. (Author) |
Journal Title | Statistics and Computing |
Journal Citation | 18 (1), pp. 73-86 |
Number of Pages | 14 |
Year | 2008 |
Place of Publication | Germany |
ISSN | 0960-3174 |
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 |
Keywords | compound Poisson distribution; generalized linear models; numerical integration; numerical acceleration; power variance function |
ANZSRC Field of Research 2020 | 490599. 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. |
Byline Affiliations | 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
Download files
2510
total views1023
total downloads0
views this month0
downloads this month