Algo\(\left(0<\alpha<1\right)\)
  1. Generate \(U\).
  2. Compute \(x=-2\ln\left(1-U^{\frac{1}{\alpha}}\right)\)
  3. Generate \(V\) from uniform(0,1), independent of U.
  4. If \(V\le\frac{x^{\alpha-1}e^{-\frac{x}{2}}}{2^{\alpha-1}\left(1-e^{-\frac{x}{2}}\right)^{^{\alpha-1}}}\) accept \(x\), otherwise go to 1.

Algorithm 2\citep*{Kundu2007}

The above algorithm was true for all \(x>0\) but for \(1<x<\infty\) it was not quite sharp. Hence this algorithm uses the following majorization function