# AICtweedie

0th

Percentile

##### Tweedie Distributions

The AIC for Tweedie glms

Keywords
models
##### 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

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.

##### 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. 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. 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.

AIC

• AICtweedie
##### Examples
# NOT RUN {
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: