Exponential Distribution

This is a special case of the Gamma (and Erlang) distributions with shape parameter \(\left(\alpha=1\right)\) and the same location and scale parameters. The standard form is therefore ( \(x\geq0\) )

\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*}

\[\mu_{n}^{\prime}=n!\]

\[M\left(t\right)=\frac{1}{1-t}\]

\begin{eqnarray*} \mu & = & 1\\ \mu_{2} & = & 1\\ \gamma_{1} & = & 2\\ \gamma_{2} & = & 6\\ m_{d} & = & 0\end{eqnarray*}

\[h\left[X\right]=1.\]

Implementation: scipy.stats.expon