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Wald Distribution¶
Special case of the Inverse Normal with shape parameter set to \(1.0\). It has support \(x\geq0\).
\begin{eqnarray*} f\left(x\right) & = & \frac{1}{\sqrt{2\pi x^{3}}}\exp\left(-\frac{\left(x-1\right)^{2}}{2x}\right).\\ F\left(x\right) & = & \Phi\left(\frac{x-1}{\sqrt{x}}\right)+\exp\left(2\right)\Phi\left(-\frac{x+1}{\sqrt{x}}\right)\\ G\left(q;\mu\right) & = & F^{-1}\left(q;\mu\right)\end{eqnarray*}
\begin{eqnarray*} \mu & = & 1\\ \mu_{2} & = & 1\\ \gamma_{1} & = & 3\\ \gamma_{2} & = & 15\\ m_{d} & = & \frac{1}{2}\left(\sqrt{13}-3\right)\end{eqnarray*}
Implementation: scipy.stats.wald