A Variance Equality Test for Two Correlated Complex Gaussian Variables With Application to Spectral Power Comparison

Abstract

Complex-valued Gaussian distributions occur frequently in signal processing. We derive a simple statistic, independent of any complex-valued correlation, for testing for the equality of variances using a sample drawn from such a bivariate distribution. The percentage points of the distribution are easy to compute. The power of the test is determined and shown to be high even for very small sample sizes when the variables are highly correlated. The new test is used to determine whether the spectral power associated with an ultralow-frequency wave in the solar magnetic field is equal at two different observing spacecraft