where \(c\ =\ \left(\frac{8}{3}\right)^{\frac{1}{2}}\) and \(b=\alpha-1+\left(\frac{3}{2}\right)c\left(\alpha+c\alpha^{\frac{1}{2}}\right)^{\frac{1}{2}}\).
In the following majorizing function \(g\left(x\right)\) is in \(\left(-\infty,\ b\right)\) and \(h\left(x\right)+g\left(x\right)\ in\ \left[b,\infty\right)\). However, all \(x\) from  \(g\left(x\right)\) are discarded if they are outside \(\left[0,b\right]\).
Algo(\(\alpha>1\))
  1. Set\(\mu=\alpha-1,\ \sigma\ =\ \left(\alpha+1.63299316185545\alpha^{\frac{1}{2}}\right)^{^{\frac{1}{2}}},\ d=2.44948974278318\sigma\) and \(b=\mu+d\).(The constants are(8/3)1/2 and 61/2)
  2. Generate \(U\). If \(U\le0.009572265238289\) go to 5.(The constant is \(\beta\))
  3. Take a sample s from the standard normal distribution and set \(x=\mu+\sigma s\). If \(x<0\ or\ x>b\) go to 2.
  4. Generate \(v\). If \(\ln\left(u\right)>\mu\left(1+\ln\left(\frac{x}{\mu}\right)\right)-x-\frac{s^2}{2}\) go to 2, otherwise deliver \(x\).
  5. Take samples from s from the standard exponential distribution and set \(x=b\left(1+\frac{s}{d}\right)\).
  6. Generate \(v\). If  \(\ln\left(u\right)>\mu\left(2+\ln\left(\frac{x}{\mu}\right)-\frac{x}{b}\right)+3.7203284924588-b-\ln\left(\frac{\sigma d}{b}\right)\) go to 2, otherwise deliver x.(The constant is \(-\ln\left(\frac{\left(2\pi\right)^{\frac{1}{2}}\beta}{1-\beta}\right)\))

Algorithm 1\citep*{KUNDU20072796}

This algorithm uses generalized exponential distribution\(\left(f_{GE}\left(x;\alpha,\lambda\right)\right)\) to generate gamma random number\(\left(f_{GA}\left(x;\alpha\right)\right)\). It proposes,