Parameterizations 0 and 1 use notation from unknown source

[ragibson]

Where does the notation for your first two parameterizations come from?

https://github.com/josemiotto/pylevy/blob/64c525f273d00d89cbbe531a6557b17b74d18f88/levy/__init__.py#L61-L63

The documentation says this is "in the notation of Nolan", but this appears to be incorrect. He seems to use "alpha, beta, gamma, delta" notation: S(α,β,γ,δ;0) and S(α,β,γ,δ;1).

I've also seen some parameterizations c and mu in place of gamma and delta, respectively. Notably, these notation conventions seem to have the distribution scale come before the location, whereas pylevy does the opposite.

[josemiotto]

Nolan calls it gamma and delta and I call them my and sigma, without loss. Where have you seen the other parameterizations?

[ragibson]

Voit's "The Statistical Mechanics of Financial Markets" uses

and e.g. Wikipedia introduces stable distributions with

but I'm not actually sure where this comes from originally (the sources here don't appear to use this notation).

[josemiotto]

I see, thanks for the Volt reference. I follow Nolan parametrization since this is the most quoted thing on Google Scholar. Personally, I'm not happy with that, because it's from a chapter of an unpublished book. I'd rather have Zolotarev as a reference, but I would agree in that it's a bit obscure to read.

I'm not sure about the following statement, but I think that because this distribution is stable, the order of location and scale may be irrelevant, like in the Normal distribution.