The rejection algorithm is based on the following property:

• if and only if and .

The idea of the ratio-of-uniform method is based on the following property: if , then . This can be shown from the change of variable , , i.e. , .

A simple generalisation of this result is: if , then where and .

As far as I can see, these methods can only be interesting if or are easy to simulate when and . This is very linked to rejection algorithm…

• ratio-of-uniform method
• Generalisation of the ratio-of-uniform method