Novel robust Gaussianity test for sparse data

In this paper, a fundamental but important statistical signal processing characteristic, namely the Gaussianity or normality, is studied. In contrast to the existing conventional Gaussianity measures, we propose a novelmeasure, which is based on Kullback-Leibler divergence (KLD) between the Gaussian probability density function (PDF) and the generalized Gaussian PDF incorporated with the skewness for the normality test. In our studies, conventional normality tests may often not be robust when they are employed for the non-Gaussian processes with symmetric PDFs. We call this new test as the KGGS test. Our proposed KGGS test is heuristically justified to be more robust than the conventional tests for different PDFs, especially for the symmetric PDFs.