The problem of fingerprint individuality is as follows: Given a sample fingerprint, what is the probability of finding a sufficiently similar fingerprint in a target population? In this paper, we develop a family of finite mixture models to represent the distribution of minutiae locations and directions in fingerprint images, including clustering tendencies and dependencies in different regions of the fingerprint domain. These models are shown to be a better fit to the observed distribution of minutiae features and give better assessments of fingerprint individuality compared to previous models. Estimates of fingerprint individuality are obtained using the probability of a random correspondence (PRC). For the "12-point match" criteria, a PRC of 9.2?10^-5 was obtained for the FVC2002 DB1 database when the number of query and template minutiae features both equal 26. The corresponding PRC based on the MSU VERIDICOM database for the same matching criteria is 6.6 ? 10^-4.