Expected Number of Maxima and Minima of a Stationary Random Process with Non-Gaussian Frequency Distribution

A method is outlined for calculating the expected number of maxima or minima of a random process with non-Gaussian frequency distribution from the statistical moments of the process and its first two derivatives. This method is based on an estimate of the joint frequency function of the process and its first two derivatives given by mesm of a generalized form of Edgeworth's series; the procedure thus consists essentially in applying a correction to the results for a Gaussian process. The functions required in this procedure are calculated for the first two correction terms; therefore, the effects of skewness and kurtosis can be calculated, provided the required moments are known. Expressions are given for these moments in terms of multiple correlation functions and multi-spectra, and the relations between these functions for a random output of a linear system and those for the random input are indicated.