Generating random numbers from a distribution specified by its Laplace transform
Statistics and Computing
On the measure and the estimation of evenness and diversity
Computational Statistics & Data Analysis
Likelihood-based and Bayesian methods for Tweedie compound Poisson linear mixed models
Statistics and Computing
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The Tweedie family of distributions is a family of exponential dispersion models with power variance functions V(μ)=μ p for $p\not\in(0,1)$ . 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.