I have this Weibull density function,
$ f(x) = 0.25 \left| 1-x \right|^{-0.5} \exp(-\left| 1-x \right|^{0.5})$
Because of the absolute value, this is split into 2 cases.
Its cumulative function
$F(a)=\int f(x) \; dx = \begin{cases} \frac{1}{2} e^{-\left( 1-a \right)^{0.5}} -\frac{1}{2} e^{-1} & 0
I take a=$\infty$, this cdf doesn't integrate to 1??
$\left[1-\frac{1}{2} e^{-(a-1)^{0.5}} - \frac{1}{2} e^{-1}\right]_1^\infty = 1 - \frac{1}{2} e^{-1}$ What is wrong?