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

Inverse Normal (Inverse Gaussian) Distribution Johnson SB Distribution