Statististics of the SK estimator

Spectral Kurtosis (SK) is a statistical approach for detecting and removing radio frequency inter- ference (RFI) in radio astronomy data. In this study, 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 es- sential to defining the thresholds for RFI discrimination. It is shown that, for a number of ac- cumulated 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 Do- main Kurtosis (TDK) estimator, whose PDF correspond