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For testing goodness of fit it is very popular to use either the chi squarestatistic or G statistics (information divergence). Asymptotically both are chisquare distributed so an obvious question is which of the two statistics thathas a distribution that is closest to the chi square distribution.Surprisingly, when there is only one degree of freedom it seems like thedistribution of information divergence is much better approximated by a chisquare distribution than the chi square statistic. For random variables weintroduce a new transformation that transform several important distributionsinto new random variables that are almost Gaussian. For the binomialdistributions and the Poisson distributions we formulate a general conjectureabout how close their transform are to the Gaussian. The conjecture is provedfor Poisson distributions.

Information Divergence is more chi squared distributed than the chi squared statistics