Generalized Exponential Distribution¶

Three positive shape parameters for \(x\geq0.\) Note that \(a,b,\) and \(c\) are all \(>0.\)

\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*}