Probability Weighted Moments

Need Help Finding The First 4 PWM of the generalized normal distribution

f(x)= $ \frac{1}{\alpha\sqrt{2\pi}}e^{ky-\frac{y^2}{2}} $

where
$ y= -k^{-1}log(1-k(x-\epsilon)/\alpha) $
$ \epsilon+\frac{\alpha}{k}<x< \infty $
F(x)= $ \int^{y}_{-\infty} e^{\frac{-t^2}{2}}~dt $