This article presents an overview of several measures for speaker recognition. These measures relate to second-order statistical tests, and can be expressed under a common formalism. Alternate formulations of these measures are given and their mathematical properties are studied. In their basic form, these measures are asymmetric, but they can be symmetrized in various ways. All measures are tested in the framework of text-independent closed-set speaker identification, on 3 variants of the TIMIT database (630 speakers) : TIMIT (high quality speech), FTIMIT (a restricted bandwidth version of TIMIT) and NTIMIT (telephone quality). Remarkable performances are obtained on TIMIT but the results naturally deteriorate with FTIMIT and NTIMIT. Symmetrization appears to be a factor of improvement, especially when little speech material is available. The use of some of the proposed measures as a reference benchmark to evaluate the intrinsic complexity of a given database under a given protocol is finally suggested as a conclusion to this work.