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Asymptotic Expansions for the Bingham Distribution
Author(s) -
Kent John T.
Publication year - 1987
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2347545
Subject(s) - mathematics , asymptotic distribution , distribution (mathematics) , calculus (dental) , econometrics , statistics , mathematical economics , mathematical analysis , estimator , medicine , dentistry
SUMMARY Statistical estimation for the Bingham distribution on the sphere requires the calculation of the normalization constant and its derivatives. The usual Taylor series expansion in two variables is useful only if the parameter values are not too large. The asymptotic series developed here enable the normalization constant to be easily and accurately evaluated when one or both of the parameter values is large.