Archive for numerical derivation

g-and-k [or -h] distributions

Posted in Statistics with tags , , , , , , , , , on July 17, 2017 by xi'an

Dennis Prangle released last week an R package called gk and an associated arXived paper for running inference on the g-and-k and g-and-h quantile distributions. As should be clear from an earlier review on Karian’s and Dudewicz’s book quantile distributions, I am not particularly fond of those distributions which construction seems very artificial to me, as mostly based on the production of a closed-form quantile function. But I agree they provide a neat benchmark for ABC methods, if nothing else. However, as recently pointed out in our Wasserstein paper with Espen Bernton, Pierre Jacob and Mathieu Gerber, and explained in a post of Pierre’s on Statisfaction, the pdf can be easily constructed by numerical means, hence allows for an MCMC resolution, which is also a point made by Dennis in his paper. Using the closed-form derivation of the Normal form of the distribution [i.e., applied to Φ(x)] so that numerical derivation is not necessary.