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Inverted Weibull Distribution¶
There is one shape parameter \(c>0\) and the support is \(x\geq0\) . Then
\begin{eqnarray*} f\left(x;c\right) & = & cx^{-c-1}\exp\left(-x^{-c}\right)\\ F\left(x;c\right) & = & \exp\left(-x^{-c}\right)\\ G\left(q;c\right) & = & \left(-\log q\right)^{-1/c}\end{eqnarray*}
\[h\left[X\right]=1+\gamma+\frac{\gamma}{c}-\log\left(c\right)\]
where \(\gamma\) is Euler’s constant.
Implementation: scipy.stats.invweibull