A new approach to Sheppard's corrections

A very simple closed-form formula for Sheppard's corrections is recovered by means of the classical umbral calculus. By means of this symbolic method, a more general closed-form formula for discrete parent distributions is provided and the generalization to the multivariate case turns to be straightforward. All these new formulae are particularly suited to be implemented in any symbolic package.
Comment: In press on Math. Meth. in Stat. MAPLE procedures available on MAPLE Application Center http://www.maplesoft.com/applications/