An earlier thread discussed the implementation of the Tukey-Lambda distrition, and I’m wondering if anyone has similarly implemented the Generalized Lambda distribution? (for R code defining the pdf, see here)

Is this also called the Tukey h distribution in some literature? If so then our GSOC intern for 2021 worked on implementing something like this in Stan through a LambertW transform

See relevant paper below

Thanks, but I don’t think they’re obviously related. The GLD is a 4-parameter distribution defined by the inverse-CDF:

(eq image from here)

Where \lambda_1 is a location parameter, \lambda_2 is a positive-constrained scale parameter, and \lambda_3 & \lambda_4 are shape parameters.

While Tukey’s G-H is is also defined by 4 parameters, location, scale (of a normal) plus shape and tail-heaviness, implemented as a normal random variate transformed by:

(eq image from here)

Maybe I’m too mathematically inept to see a link, but after playing with `gld::dgl()`

and `tukeyGH::dgh()`

in R, they feel like each has a distinct set of curves that the other can’t replicate, and I find the GLD curves a bit more intuitive feeling.

I think @bgoodri put this together for his Stancon 2020 talk. See StanCon2020/quantile_functions.stan at 277489d6a9367749a4c683c1fab2c1a2eaf32013 · bgoodri/StanCon2020 · GitHub

Oh, good find!