.. _continuous-johnsonsu:

Johnson SU Distribution

There are two shape parameters :math:a\in\mathbb{R} and :math:b>0, and the support is :math:x\in\mathbb{R}.

.. math:: :nowrap:

\begin{eqnarray*} f\left(x;a,b\right) & = & \frac{b}{\sqrt{x^{2}+1}}\phi\left(a+b\log\left(x+\sqrt{x^{2}+1}\right)\right)\\
F\left(x;a,b\right) & = & \Phi\left(a+b\log\left(x+\sqrt{x^{2}+1}\right)\right)\\
G\left(q;a,b\right) & = & \sinh\left(\frac{\Phi^{-1}\left(q\right)-a}{b}\right)\end{eqnarray*}

Implementation: scipy.stats.johnsonsu