.. _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