Add tweedie distribution

[kellijohnson-NOAA]

Currently only gamma and lognormal are fully supported. Adding support for the newly implemented Tweedie distribution in VAST will allow for a more-complete set of comparisons with {sdmTMB}.

ObsModel = c(10, 2)
RhoConfig = c(Beta1 = 3, Beta2 = 0, Epsilon1 = 0, Epsilon2 = 0)
FieldConfig= c(Omega1 = 0, Epsilon1 = 0, Omega2 = "IID", Espilon2 = "IID")

Notes for code changes

• 10 is for the Tweedie distribution
• Turn off random-effects for temporal variation in the first intercept RhoConfig["Beta1"]=3 as documented in VAST::check_fit()
• Using 0 for all ...1 parameters turns them off for the first model, which makes sense because there is only one model with the Tweedie distribution.

Definition/Explanation of Tweedie

The Tweedie distribution is a special case of an exponential distribution.
It can have a cluster of data items at zero (called a “point mass”),
which is particularly useful for modeling claims in the insurance industry,
in medical/genomic testing, or
anywhere else there is a mixture of zeros and non-negative data points.
Basically, if you see a histogram with a spike at zero,
it’s a possible candidate to be fitted to a Tweedie model.

[James-Thorson-NOAA]

In case you're interested in more theory for the Tweedie, see e.g., https://doi.org/10.1002/ecy.3637, and I also have a paper in review (with Tim Miller and Brian Stock) about how it arises naturally for comp-data via the hierarchical expansion of counted animals. obviously the Poisson-link delta model is still a more flexible generalization that requires little extra computation time.

[kellijohnson-NOAA]

Thanks Jim!