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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