A bulk Lennard-Jones fluid was simulated using the grand canonical Mon
te Carlo method. Three different sampling methods were used in the tra
nsition matrix, namely the Metropolis, Barker and a third novel method
. While it can be shown that the Metropolis method will give the most
accurate ensemble averages in the limit of an infinitely long run, the
new method termed ''Modified Barker Sampling'' (MBS), is shown to be
superior for the runs of practical length for the particular system st
udied.