This is documentation for an old release of SciPy (version 1.4.1). Read this page in the documentation of the latest stable release (version 1.15.1).
Double Gamma Distribution¶
The double gamma is the signed version of the Gamma distribution. For \(\alpha>0:\)
\begin{eqnarray*} f\left(x;\alpha\right) & = & \frac{1}{2\Gamma\left(\alpha\right)}\left|x\right|^{\alpha-1}e^{-\left|x\right|}\\
F\left(x;\alpha\right) & = & \left\{
\begin{array}{ccc}
\frac{1}{2}-\frac{\gamma\left(\alpha,\left|x\right|\right)}{2\Gamma\left(\alpha\right)} & & x\leq0\\
\frac{1}{2}+\frac{\gamma\left(\alpha,\left|x\right|\right)}{2\Gamma\left(\alpha\right)} & & x>0
\end{array}
\right.\\
G\left(q;\alpha\right) & = & \left\{
\begin{array}{ccc}
-\gamma^{-1}\left(\alpha,\left|2q-1\right|\Gamma\left(\alpha\right)\right) & & q\leq\frac{1}{2}\\
\gamma^{-1}\left(\alpha,\left|2q-1\right|\Gamma\left(\alpha\right)\right) & & q>\frac{1}{2}
\end{array}
\right.\end{eqnarray*}
\[M\left(t\right)=\frac{1}{2\left(1-t\right)^{a}}+\frac{1}{2\left(1+t\right)^{a}}\]
\begin{eqnarray*} \mu=m_{n} & = & 0\\
\mu_{2} & = & \alpha\left(\alpha+1\right)\\
\gamma_{1} & = & 0\\
\gamma_{2} & = & \frac{\left(\alpha+2\right)\left(\alpha+3\right)}{\alpha\left(\alpha+1\right)}-3\\
m_{d} & = & \mathrm{NA}\end{eqnarray*}
Implementation: scipy.stats.dgamma