tweedie.convert {tweedie}

Convert Tweedie parameters

Description

Converts Tweedie distribution parameters to the parameters of the underlying distributions

Usage

	tweedie.convert( xi=NULL, mu, phi, power=NULL)

Arguments

xi

the value of \xi such that the variance is \mbox{var}[Y]=\phi\mu^{\xi}

power

a synonym for \xi

mu

the mean

phi

the dispersion

Details

The Tweedie family of distributions with 1<\xi<2 is the Poisson sum of gamma distributions (where the Poisson distribution has mean \lambda, and the gamma distribution has scale and shape parameters). When used to fit a glm, the model is fitted with the usual glm parameters: the mean \mu and the dispersion parameter \phi. This function converts the parameters (p, \mu, \phi) to the values of the parameters of the underlying Poisson distribution \lambda and gamma distribution (scale and shape parameters).

Value

a list containing the values of the mean of the underlying Poisson distribution (as poisson.lambda), the scale parameter of the underlying gamma distribution (as gamma.scale), the shape parameter of the underlying gamma distribution (as gamma.shape), the probability of obtaining a zero response (as p0), the mean of the underlying gamma distribution (as gamma.mean), and the dispersion parameter of the underlying gamma distribution (as gamma.phi).

Author(s)

Peter Dunn ([e-mail])

References

Dunn, P. K. and Smyth, G. K. (2008). Evaluation of Tweedie exponential dispersion model densities by Fourier inversion. Statistics and Computing, 18, 73–86. doi: 10.1007/s11222-007-9039-6

Dunn, Peter K and Smyth, Gordon K (2005). Series evaluation of Tweedie exponential dispersion model densities Statistics and Computing, 15(4). 267–280. doi: 10.1007/s11222-005-4070-y

Dunn, Peter K and Smyth, Gordon K (2001). Tweedie family densities: methods of evaluation. Proceedings of the 16th International Workshop on Statistical Modelling, Odense, Denmark, 2–6 July

Tweedie, M. C. K. (1984). An index which distinguishes between some important exponential families. Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference (Eds. J. K. Ghosh and J. Roy), pp. 579-604. Calcutta: Indian Statistical Institute.

See Also

dtweedie.saddle

Examples

tweedie.convert(xi=1.5, mu=1, phi=1)