AICtweedie: Tweedie Distributions

In tweedie: Evaluation of Tweedie Exponential Family Models

Tweedie Distributions

Description

The AIC for Tweedie glms

Usage

	AICtweedie( glm.obj, dispersion=NULL, k = 2, verbose=TRUE)

Arguments

glm.obj	a fitted Tweedie glm object
dispersion	the dispersion parameter phi; the default is NULL which means to use an estimate
k	numeric: the penalty per parameter to be used; the default is k=2
verbose	if TRUE (the default), a warning message is produced about the Poisson case; see the second Note below

Details

See AIC for more details on the AIC; see dtweedie for more details on computing the Tweedie densities

Value

Returns a numeric value with the corresponding AIC (or BIC, depending on k)

Note

Computing the AIC may take a long time.

Note

Tweedie distributions with the index parameter as 1 correspond to Poisson distributions when phi=1. However, in general a Tweedie distribution with an index parameter equal to one may not be referring to a Poisson distribution with phi=1, so we cannot assume that phi=1 just because the index parameter is set to one. If the Poisson distribution is intended, then dispersion=1 should be specified. The same argument applies for similar situations.

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

Jorgensen, B. (1997). Theory of Dispersion Models. Chapman and Hall, London.

Sakamoto, Y., Ishiguro, M., and Kitagawa G. (1986). Akaike Information Criterion Statistics. D. Reidel Publishing Company.

See Also

AIC

Examples

library(statmod) # Needed to use  tweedie  family object

### Generate some fictitious data
test.data <- rgamma(n=200, scale=1, shape=1)

### Fit a Tweedie glm and find the AIC
m1 <- glm( test.data~1, family=tweedie(link.power=0, var.power=2) )

### A Tweedie glm with p=2 is equivalent to a gamma glm:
m2 <- glm( test.data~1, family=Gamma(link=log))

### The models are equivalent, so the AIC shoud be the same:
AICtweedie(m1)
AIC(m2)

tweedie documentation built on Aug. 17, 2022, 9:06 a.m.