Quick looks at dispersal. Lewis et al 2008 show how to calculate empirical moment generating functions, but I’m not sure how useful that is for us. Nathan et al. 2012 has a good review of kernels, but not much statistical info. I found Viana et al. 2016 which suggests fitting the CDF is better than fitting the PDF.
Viana also led my to the fitdistrplus package, which fits standard distributions. I think this is what we need–I was increasinglyl unconfident im my home-rolled fitting routines. The only rub is that I’ll need to write d, p and q functions for any “special” distributions (e.g., 2Dt).