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In this work, we compare five different methods proposed in forensic statistics to cope with the rare type match problem. This problem arises when the DNA profile of a suspect coincides with the profile from a crime sample, but it is not present in the available database collected from the population of reference. We compare the methods, designed to evaluate the likelihood ratio, by using a set of supervised cases and by considering each method as a classifier that provides the posterior probabilities of two alternative hypotheses, those of the prosecution and the defense, starting form a grid of prior probabilities. We compare the methods using the value of the posterior cross entropy, evaluated for each them using the set of cases, and decompose it into two terms quantifying their calibration and refinement loss.