Log-cumulants-based Edgeworth expansion for skew-distributed aggregate interference

Abstract

The Edgeworth expansion approximates nearly Gaussian distributions in terms of cumulants. This expansion is developed within the framework of First Kind Statistics, where definitions are derived from the Fourier transform. Alternatively, the framework of Second Kind Statistics offers analogous definitions which are derived from the Mellin transform. Although a formalism with such similarity to the existing definitions cannot lead to intrinsically new results, statistical methods within this new framework has been understudied. This paper introduces an Edgeworth expansion in terms of log-cumulants, which are the analogous to cumulants for the Second Kind statistics. More importantly, this new expansion approximates asymmetric distributions which are commonly-found in aggregate interference modeling.