Quantitative Description of Non-Gaussian Random Signals

Abstract

The amplitude statistics of a continuous random signal are often expressed by the probability density. If the signal is Gaussian or normal, the well-known exponential equation and bell-shaped curve define these statistics. If the signal is non-Gaussian, but does not deviate from the Gaussian by too large a margin, either the Gram-Charlier or the Edgeworth series may be used to describe the signal and the amount of nonnormality. The amount of nonnormality is expressed in terms of the third and fourth statistical moments utilized in these series, which are called skewness and kurtosis, respectively. In this paper, the abbreviated Gram-Charlier and Edgeworth series are used to determine the amplitude probability density and the corresponding probability distribution as functions of skewness and kurtosis. Graphical results supplement the equations.