论文信息 - On the derivatives of the normalising constant of the Bingham distribution

On the derivatives of the normalising constant of the Bingham distribution

It is shown that an arbitrary joint partial derivative of the Bingham normalising constant, expressed in standard form, is proportional to the normalising constant of a Bingham distribution of higher dimension. Two consequences of this result are noted.

Andrew T. A. Wood | Alfred Kume | A. Wood | A. Kume

[1] K. Mardia,et al. Statistical Shape Analysis , 1998 .

[2] A. Wood,et al. Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants , 2005 .

[3] Christopher Bingham. An Antipodally Symmetric Distribution on the Sphere , 1974 .

[4] K. Mardia,et al. Maximum Likelihood Estimators for the Matrix Von Mises-Fisher and Bingham Distributions , 1979 .

[5] J. Kent. The Complex Bingham Distribution and Shape Analysis , 1994 .

[6] R. Muirhead. Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.