The discrepancy distribution of stationary multiplier rules for rounding probabilities

Abstract.

The problem of rounding finitely many (continuous) probabilities to (discrete) proportions N _i/n is considered, for some fixed rounding accuracy n. It is well known that the rounded proportions need not sum to unity, and instead may leave a nonzero discrepancy D=(∑N _i) −n. We determine the distribution of D, assuming that the rounding function used is stationary and that the original probabilities follow a uniform distribution.