AICtweedie: Tweedie Distributions

Description

The AIC for Tweedie glms

Usage

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

Value

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

Arguments

glm.obj: a fitted Tweedie glm object
dispersion: the dispersion parameter $ϕ$ ; 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

Author

Peter Dunn (pdunn2@usc.edu.au)

Details

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

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. tools:::Rd_expr_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. tools:::Rd_expr_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.

Examples

Run this code

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)

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