A new approach to Sheppard's corrections
Elvira Di Nardo
TL;DR
This paper introduces a simplified, symbolic approach to Sheppard's corrections using umbral calculus, providing new formulas for discrete and multivariate cases that are easy to implement.
Contribution
It presents a novel, closed-form formula for Sheppard's corrections via umbral calculus and extends it to discrete and multivariate distributions.
Findings
Simplified closed-form Sheppard's corrections formula
Generalized formulas for discrete distributions
Straightforward extension to multivariate cases
Abstract
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.
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Taxonomy
TopicsDiverse Scientific and Engineering Research · Scientific Research and Discoveries · Bayesian Methods and Mixture Models