UPPER BOUNDS FOR THE EXPECTED JEFFERSON ROUNDING UNDER
MEAN-VARIANCE-SKEWNESS CONDITIONS

Abstract: For the class of nonnegative random variables with given mean, variance, and
skewness and support bound, we present a sharp upper bound for the expectation of rounding
due to the Jefferson rule. The result gives an estimate for average extra gains due to rounding
down payments. Arguments of four-dimensional geometric moment theory implemented in
the proof provide tools for refined evaluations of rates of convergence of probability
distributions and positive linear operators.

1991 AMS Mathematics Subject Classification: Primary 60E15, 62P10; Secondary
90A28.

Key words and phrases: Gain of rounding, Jefferson rounding, mean-variance-skewness
and support constraints, geometric moment theory, four-dimensional geometry.