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.

See Also

AIC

Aliases
  • 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:
m2 <- glm( test.data~1, family=Gamma(link=log))

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

# }
Documentation reproduced from package tweedie, version 2.3.2, License: GPL (>= 2)

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