I know that the instantaneous discriminating information (i.e., the LLR) when the data statistics for both H1 and H0 data are Cauchy recovers finite informational means, since the generalized SNR=K-L divergence (i.e., 1 - 0) is well defined.  Has anyone worked out the two associated densities of the actual LLR statistic, or, alternatively, is it known which other of its moments are finite?