Kume, A. and Wood, ATA (2005) Saddlepoint approximations for the Bingham and Fisher-Bingham normalising constants. Biometrika, 92 (2). pp. 465-476. ISSN 0006-3444.
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The Fisher-Bingham distribution is obtained when a multivariate normal random vector is conditioned to have unit length. Its normalising constant can be expressed as an elementary function multiplied by the density, evaluated at 1, of a linear combination of independent noncentral chi(1)(2) random variables. Hence we may approximate the normalising constant by applying a saddlepoint approximation to this density. Three such approximations, implementation of each of which is straightforward, are investigated: the first-order saddlepoint density approximation, the second-order saddlepoint density approximation and a variant of the second-order approximation which has proved slightly more accurate than the other two. The numerical and theoretical results we present show that this approach provides highly accurate approximations in a broad spectrum of cases.
|Uncontrolled keywords:||complex Bingham distribution; directional data; shape analysis; von Mises-fisher distribution; Watson distribution|
|Subjects:||H Social Sciences > HA Statistics|
|Divisions:||Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science|
|Depositing User:||Judith Broom|
|Date Deposited:||19 Dec 2007 18:19|
|Last Modified:||14 Jan 2010 13:58|
|Resource URI:||http://kar.kent.ac.uk/id/eprint/540 (The current URI for this page, for reference purposes)|
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