Statistics of the Spectral Kurtosis Estimator

Spectral kurtosis (SK) is a statistical approach for detecting and removing radio-frequency interference (RFI) in radio astronomy data. In this article, the statistical properties of the SK estimator are investigated and all moments of its probability density function are analytically determined. These moments provide a means to determine the tail probabilities of the estimator that are essential to defining the thresholds for RFI discrimination. It is shown that, for a number of accumulated spectra M >= 24, the first SK standard moments satisfy the conditions required by a Pearson type IV probability density function (pdf), which is shown to accurately reproduce the observed distributions. The cumulative function (CF) of the Pearson type IV is then found, in both analytical and numerical forms, suitable for accurate estimation of the tail probabilities of the SK estimator. This same framework is also shown to be applicable to the related time-domain kurtosis (TDK) estimator, whose pdf corresponds to Pearson type IV when the number of time-domain samples is M >= 46. The pdf and CF also are determined for this case.