Negative Weibull distribution (${\Psi }_{\alpha }$)

For $\alpha >0$, the standard negative Weibull distribution has distribution function ${\Psi }_{\alpha }(x)=e^{-(-x{)}^{\alpha }}$ for $x<0$ and one for $x\ge 0$. This is the probability distribution of the negative of a standard positive Weibull distribution variable.