  Generation of pseudorandom numbers from different probability distributions
has been studied extensively in the Monte Carlo simulation literature. Two
standard generation techniques are the acceptance-rejection and inverse
transformation methods. An alternative approach to Monte Carlo simulation is
the quasi-Monte Carlo method, which uses low-discrepancy sequences, instead of
pseudorandom numbers, in simulation. Low-discrepancy sequences from different
distributions can be obtained by the inverse transformation method, just like
for pseudorandom numbers. In this paper, we will present an
acceptance-rejection algorithm for low-discrepancy sequences. We will prove a
convergence result, and present error bounds. We will then use this
acceptance-rejection algorithm to develop quasi-Monte Carlo versions of some
well known algorithms to generate beta and gamma distributions, and investigate
the efficiency of these algorithms numerically. We will also consider the
simulation of the variance gamma model, a model used in computational finance,
where the generation of these probability distributions are needed. Our results
show that the acceptance-rejection technique can result in significant
improvements in computing time over the inverse transformation method in the
context of low-discrepancy sequences.
