Fisherian statistical parameters are frequently published for paleomagnetic data that form elongate directional distributions, despite the fact that they are strictly applicable to circularly symmetric distributions. Thus the Binham statistical parameters provide better approximation to elongate paleomagnetic data sets. Because the Bingham parameters also pertain to directions dispersed along a great circle, they supply a statistical basis for describing the distribution of axes perpendicular to great circles intersecting at a common point, a problem that arises in the analysis of multicomponent magnetization, in the application of the Hargraves' correction technique, and in intersecting lunes. Application of the Bingham density function to paleomagnetic poles from Tertiary lava flows in Iceland reveals temporal fluctuations in the eccentricity of the data. Use of the Bingham density function in the analysis of intersecting great circles is illustrated by application to data from a lightning strike remagnetized basalt in northern Arizona. Statistical methods for analyzing paleomagnetic data were first introduced by Fisher <1953>, who used a circularly symmetric density function for spherical distributions that is analogous to a two-dimensional Gaussian distribution. The theory was designed to describe the distribution of remanent magnetization directions for samples collected from a homogeneously magnetized rock unit, where the dispersion was generated by random processes. Subsequently developed laboratory demagnetization techniques have shown that frequently this not the case, but that the magnetic vectors within a set of specimens even from a single unit may be a varying mixture of two or more superimposed magnetic components; hence the directional distributions of such samples frequently may be non-Fisherian. The Fisher distribution has also been extended to the treatment of average directions from sites or geologic formations with different ages of magnetization where non-Fisherian directional densities may also arise, because of the intricate temporal shifts in the direction of the geomagnetic field. The complexity of rock magnetic and geomagnetic processes generally precludes definition by any single theoretical model that might provide statistical parameters describing the distribution of resultant vectors. Recent studies concerned with the nature of obviously non-Fisherian distributions, however, have tended to employ great circles or elliptically shaped models to describe their paleomagnetic data sets . Depending on the values of its parameters, the Bingham distribution may be circularly symmetric, elliptically shaped, or dispersed along a great circle; thus the application of the Bingham distribution function to these situations appears quite appropriate. In this article the Bingham distribution is introduced and briefly described. A discussion of the applicability of Bingham statistics to the analysis of paleomagnetic poles and directions and to intersecting great circles is then presented, followed by a few illustrative examples.