Exponential DistributionΒΆ
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