Open AccessEstimation of the Bingham distribution function on nearly two‐dimensional data sets
Author(s) -
Gillett Stephen L.
Publication year - 1986
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1986.tb04375.x
Subject(s) - bessel function , mathematics , limit (mathematics) , interpolation (computer graphics) , eigenvalues and eigenvectors , distribution (mathematics) , mathematical analysis , function (biology) , point (geometry) , distribution function , geometry , physics , classical mechanics , motion (physics) , quantum mechanics , evolutionary biology , biology
Summary. In cases where directional data, such as palaeomagnetic directions, lie nearly along a great circle, a good approximation to the maximum likelihood estimate of the intermediate concentration parameter k 2 in the Bingham probability distribution is given by: 2( t 2 / N ) – 1 = I 1 (1/2 k 2 )/ I 0 (1/2 k 2 ), where t 2 is the intermediate eigenvalue, N is the number of samples, and the I i are the appropriate modified Bessel functions of the first kind. This estimate, the asymptotic limit as the smallest eigenvalue t 1 → 0, corresponds to restricting all points to lie on a great circle. The limit is also useful as an endpoint for interpolation, especially since numerical calculation in this region is difficult.