Exponential Power Distribution¶

One positive shape parameter \(b\) . Defined for \(x\geq0.\)

\begin{eqnarray*} f\left(x;b\right) & = & ebx^{b-1}\exp\left[x^{b}-e^{x^{b}}\right]\\ F\left(x;b\right) & = & 1-\exp\left[1-e^{x^{b}}\right]\\ G\left(q;b\right) & = & \log^{1/b}\left[1-\log\left(1-q\right)\right]\end{eqnarray*}