Inverse Normal (Inverse Gaussian) Distribution#
The standard form involves the shape parameter (in most definitions, L=0.0 is used). (In terms of the regress documentation \mu=A/B ) and B=S and L is not a parameter in that distribution. A standard form is x>0
This is related to the canonical form or JKB “two-parameter” inverse Gaussian when written in it’s full form with scale parameter S and location parameter L by taking L=0 and S\equiv\lambda, then \mu S is equal to \mu_{2} where \mu_{2} is the parameter used by JKB. We prefer this form because of it’s consistent use of the scale parameter. Notice that in JKB the skew \left(\sqrt{\beta_{1}}\right) and the kurtosis ( \beta_{2}-3 ) are both functions only of \mu_{2}/\lambda=\mu S/S=\mu as shown here, while the variance and mean of the standard form here are transformed appropriately.
Implementation: scipy.stats.invgauss