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Multibiometric systems fuse information from different sources to compensate for the limitations in performance of individual matchers. We propose a framework for the optimal combination of match scores that is based on the likelihood ratio test. The distributions of genuine and impostor match scores are modeled as finite Gaussian mixture model. The proposed fusion approach is general in its ability to handle 1) discrete values in biometric match score distributions, 2) arbitrary scales and distributions of match scores, 3) correlation between the scores of multiple matchers, and 4) sample quality of multiple biometric sources. Experiments on three multibiometric databases indicate that the proposed fusion framework achieves consistently high performance compared to commonly used score fusion techniques based on score transformation and classification.