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.. _continuous-loglaplace:
Log Double Exponential (Log-Laplace) Distribution
=================================================
Defined over :math:`x>0` with :math:`c>0`
.. math::
:nowrap:
\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*}
.. math::
h\left[X\right]=\log\left(\frac{2e}{c}\right)
Implementation: `scipy.stats.loglaplace`
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