  We describe two distinct approaches to obtaining cloud point densities and
coexistence properties of polydisperse fluid mixtures by Monte Carlo simulation
within the grand canonical ensemble. The first method determines the chemical
potential distribution $\mu(\sigma)$ (with $\sigma$ the polydisperse attribute)
under the constraint that the ensemble average of the particle density
distribution $\rho(\sigma)$ matches a prescribed parent form. Within the region
of phase coexistence (delineated by the cloud curve) this leads to a
distribution of the fluctuating overall particle density n, p(n), that
necessarily has unequal peak weights in order to satisfy a generalized lever
rule. A theoretical analysis shows that as a consequence, finite-size
corrections to estimates of coexistence properties are power laws in the system
size. The second method assigns $\mu(\sigma)$ such that an equal peak weight
criterion is satisfied for p(n)$ for all points within the coexistence region.
However, since equal volumes of the coexisting phases cannot satisfy the lever
rule for the prescribed parent, their relative contributions must be weighted
appropriately when determining $\mu(\sigma)$. We show how to ascertain the
requisite weight factor operationally. A theoretical analysis of the second
method suggests that it leads to finite-size corrections to estimates of
coexistence properties which are {\em exponentially small} in the system size.
The scaling predictions for both methods are tested via Monte Carlo simulations
of a novel polydisperse lattice gas model near its cloud curve, the results
showing excellent quantitative agreement with the theory.
