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.. _continuous-expon:
Exponential Distribution
========================
This is a special case of the Gamma (and Erlang) distributions with
shape parameter :math:`\left(\alpha=1\right)` and the same location and scale parameters. The standard form is
therefore ( :math:`x\geq0` )
.. math::
:nowrap:
\begin{eqnarray*} f\left(x\right) & = & e^{-x}\\
F\left(x\right) & = & \gamma\left(1,x\right) = 1-e^{-x}\\
G\left(q\right) & = & -\log\left(1-q\right)\end{eqnarray*}
.. math::
\mu_{n}^{\prime}=n!
.. math::
M\left(t\right)=\frac{1}{1-t}
.. math::
:nowrap:
\begin{eqnarray*} \mu & = & 1\\ \mu_{2} & = & 1\\ \gamma_{1} & = & 2\\ \gamma_{2} & = & 6\\ m_{d} & = & 0\end{eqnarray*}
.. math::
h\left[X\right]=1.
Implementation: `scipy.stats.expon`
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