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The identification of unsubtracted foreground residuals in the cosmicmicrowave background maps on large scales is of crucial importance for theanalysis of polarization signals. These residuals add a non-Gaussiancontribution to the data. We propose the Kullback-Leibler (KL) divergence as aneffective, non-parametric test on the one-point probability distributionfunction of the data. With motivation in information theory, the KL divergencetakes into account the entire range of the distribution and is highlynon-local. We demonstrate its use by analyzing the large scales of the Planck2013 SMICA temperature fluctuation map and find it consistent with the expecteddistribution at a level of 6%. Comparing the results to those obtained usingthe more popular Kolmogorov-Smirnov test, we find the two methods to be ingeneral agreement.

The Kullback-Leibler Divergence as an Estimator of the Statistical Properties of CMB Maps