Inverse Normal (Inverse Gaussian) Distribution

The standard form involves the shape parameter $\mu$ (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