Convert Tweedie parameters
Converts Tweedie distribution parameters to the parameters of the underlying distributions
tweedie.convert( xi=NULL, mu, phi, power=NULL)
xi |
the value of xi such that the variance is var(Y) = phi * mu^xi |
power |
a synonym for xi |
mu |
the mean |
phi |
the dispersion |
The Tweedie family of distributions with 1 < power < 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).
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).
Peter Dunn (pdunn2@usc.edu.au)
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.
tweedie.convert(xi = 1.5, mu = 1, phi = 1)
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