Probability Distribution of Spectral Integrals

Abstract

A statistical analysis is performed to determine the probability distribution applicable to spectral integrals. This analysis shows that, since the spectrum of a stationary Gaussian random process follows a chi-square distribution, the integral of the spectrum will also be chi-squared. The number of degrees of freedom of the spectral integral depends on the shape of the spectrum. As a practical example, confidence limits are calculated for significant wave height estimates obtained by integrating the wave spectrum.