The use of antithetic control variates in computer simulations

The method of antithetic variates is a well-known technique for reducing the variability of estimators in computer simulation experiments. However, the usually suggested way of using the method, if incorrectly applied, can lead to an increase in the variance of estimators of certain quantities, such as percentiles. A procedure, based on two non-standard methods of generating samples from the normal distribution, is suggested which does not suffer this weakness. Numerical examples are given showing the ease of implementation and the effectiveness of the procedure.