  To take sample biases and skewness in the observations into account,
practitioners frequently weight their observations according to some marginal
distribution. The present paper demonstrates that such weighting can indeed
improve the estimation. Studying contingency tables, estimators for marginal
distributions are proposed under the assumption that another marginal is known.
It is shown that the weighted estimators have a strictly smaller asymptotic
variance whenever the two marginals are correlated. The finite sample
performance is illustrated in a simulation study. As an application to traffic
accident data the method allows for correcting a well-known bias in the
observed injury severity distribution.
