Generalized Exponential Distribution#

Three positive shape parameters \(a,b,c>0\) with support \(x\geq0\).

\begin{eqnarray*} f\left(x;a,b,c\right) & = & \left(a+b\left(1-e^{-cx}\right)\right)\exp\left(ax-bx+\frac{b}{c}\left(1-e^{-cx}\right)\right)\\ F\left(x;a,b,c\right) & = & 1-\exp\left(ax-bx+\frac{b}{c}\left(1-e^{-cx}\right)\right)\\ G\left(q;a,b,c\right) & = & F^{-1}\end{eqnarray*}