Once again, here’s the list of distributions, with where we are on each:
- Distributions with modes at zero:
- Exponential power (generalized normal): This is in the gnorm package, and getting start values is probably nontrivial. It is defined on the whole real line, so a “sensible” value for the location parameter (\(\mu\)) is zero. It is a generalization of the normal, Laplace, and uniform distributions. It might be better just to calculate the first two directly (I’ve already written code for a half-normal, and could do the same for the Laplace)
- 2Dt: This requires writing a function to get the CDF by numerical integration, unless I can figure out the sense in which it is related to the t distribution. Not sure how to get start values.
- Log-sech: This will require a custom formulation, like 2Dt. Cauchy is a special case, which we can use for start values.
- Inverse power: This will require a custom formulation, like 2Dt. Not sure how to get start values.
- Logistic: This works out of the box, but needs to be truncated.
- Mixture models: this is an infinitely large set; I won’t treat it here.
- Special cases of generalized inverse Gaussian. Code for this is in the rmutils package; I would have to write a wrapper for those to trap for non-numeric and vector values of \(x\). I also haven’t yet looked at how to get start values.
- Gamma: this is in the stats package:
(d)gamma. So this can be used out of the box. - Inverse Gaussian (Wald): this is in the actuar package:
(d)invgauss. This requires start values; I wrote code for this last year.
- Gamma: this is in the stats package:
- Wiebull: This is in the stats package and works out of the box.
- Lognormal: This is in the stats package and works out of the box.
I also put a bunch of effort into the generalized gamma distribution, which generalizes the gamma, Wiebull, and exponential distributions. I’ve written a function that gets the start values for non-truncated data; I’d need to do more work for the truncated distributions.
I just looked again at the empirical dispersal dists. Although theere are many the have a mode slightly away from zero, there’s only one that is far from zero; so I think we need to fit the central distributions, unfortunately.