I am reading the book Stochastic Simulation, Algorithms and Analysis by Asmussen. On page 39, when talking about inversion method for sampling a distribution, he gave an example:
an r.v. distributed as the overshoot X − a given X > a can be generated as $F^{-1} (U (1-F (a)) − a$,
where $U$ is a r.v. uniform in $[0,1]$.
But I think the distribution is $F^{-1} (U (1-F (a)) + F(a)) - a$. I was wondering which is correct and why?
Thanks and regards!