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Fingerprint singularities play an important role in several fingerprint recognition and classification systems. Although some general relationships and constraints about the location of singularities in the different fingerprint classes are well known, to the best of our knowledge no statistical models have been developed until now. This paper studies the spatial distributions of singularity locations in nature and derives, from a representative dataset of labelled samples, the probability density functions of the four main fingerprint classes. The results obtained can be directly exploited to improve the accuracy of many techniques relying on the position of singularities, as confirmed by the results of two experiments on fingerprint classification and synthesis.