Measuring Non-Gaussianity by Phi-Transformed and Fuzzy Histograms
Figure 2
Overview of the computation of : left: scatter plot of two signals in original space. On the -axis: Gaussian noise signal. On the -axis: signal with a rectangular pattern. The lines represent the quantiles assuming a Gaussian distribution; right: the scatter plot after applying the Gaussian CDF. The quantiles now form an equidistant grid. On the axes: histograms and compression costs using Huffman coding. Since the Gaussian signal does not contain any pattern beyond Gaussianity, it cannot be compressed in CDF-space.
