Log Double Exponential (Log-Laplace) DistributionΒΆ
One shape parameter \(c>0\). The support is \(x\geq0\).
\begin{eqnarray*}
f\left(x;c\right) & = & \left\{
\begin{array}{ccc}
\frac{c}{2}x^{c-1} & & 0 < x < 1 \\
\frac{c}{2}x^{-c-1} & & x \geq 1
\end{array}
\right. \\
F\left(x;c\right) & = & \left\{
\begin{array}{ccc}
\frac{1}{2}x^{c} & & 0 < x < 1 \\
1-\frac{1}{2}x^{-c} & & x \geq 1
\end{array}
\right. \\
G\left(q;c\right) & = & \left\{
\begin{array}{ccc}
\left(2q\right)^{1/c} & & 0 \leq q < \frac{1}{2} \\
\left(2-2q\right)^{-1/c} & & \frac{1}{2} \leq q \leq 1
\end{array}
\right.
\end{eqnarray*}
\[h\left[X\right]=\log\left(\frac{2e}{c}\right)\]
Implementation: scipy.stats.loglaplace