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Truncated Exponential Distribution¶
This is an exponential distribution defined only over a certain region \(0<x<B\) . In standard form this is
\begin{eqnarray*} f\left(x;B\right) & = & \frac{e^{-x}}{1-e^{-B}}\\ F\left(x;B\right) & = & \frac{1-e^{-x}}{1-e^{-B}}\\ G\left(q;B\right) & = & -\log\left(1-q+qe^{-B}\right)\end{eqnarray*}
\[\mu_{n}^{\prime}=\Gamma\left(1+n\right)-\Gamma\left(1+n,B\right)\]
\[h\left[X\right]=\log\left(e^{B}-1\right)+\frac{1+e^{B}\left(B-1\right)}{1-e^{B}}.\]
Implementation: scipy.stats.truncexpon