Affine growth of wave heights

Wave heights in oceanography are modelled using the Rayleigh, Weibull, Generalized Gamma and log-normal distributions.

Coin flips with offset returns are approximated by the normal distribution, linear returns by the log-normal and affine returns seem to be approximated by an appropriately scaled logit-normal distribution. A good fit for the wave heights is performed by this latter distribution. Perhaps because, for some cases at least, affine returns result in power law tails. Further details for Mooloolaba, Queensland are contained in a pre-print on GitHub.