We provide an algebraic setting for cumulants and factorial moments via the classical umbral calculus. Our main tools are the compositional inverse of the unity umbra, this being related to logarithmic power series, and a new umbra here introduced, the singleton umbra. We develop formulae that express cumulants, factorial moments and central moments as umbral functions.
An umbral setting for cumulants and factorial moments
DI NARDO, Elvira;
2006-01-01
Abstract
We provide an algebraic setting for cumulants and factorial moments via the classical umbral calculus. Our main tools are the compositional inverse of the unity umbra, this being related to logarithmic power series, and a new umbra here introduced, the singleton umbra. We develop formulae that express cumulants, factorial moments and central moments as umbral functions.
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