The complex Bingham distribution and shape analysis. (English) Zbl 0806.62040

Kent, John T.

J. R. Stat. Soc., Ser. B 56, No. 2, 285-299 (1994).

Let \({\mathfrak z}\) be a \(k\)-dimensional complex vector and let \({\mathfrak C}S^{k-1}= \{{\mathfrak z}\): \(|{\mathfrak z}|=1\}\) denote the unit complex sphere in \({\mathfrak C}^ k\). The complex Bingham distribution on \({\mathfrak C}S^{k-1}\) is defined by the probability density function \(f({\mathfrak z})= c(A)^{-1}\exp {\mathfrak z}^* A{\mathfrak z}\), \({\mathfrak z}\in {\mathfrak C}S^{k-1}\), where \({\mathfrak z}^*\) is the complex conjugate of the transpose of \({\mathfrak z}\). \(c(A)\) is a normalizing constant, and the parameter matrix \(A\) is a \(k\times k\) Hermitian matrix. Properties of this distribution are studied and statistical applications considered.

Reviewer: K.S.Miller (Rye Brook)

MSC:

62H10	Multivariate distribution of statistics
62H99	Multivariate analysis
60E99	Distribution theory

Keywords:

shape analysis; unit complex sphere; complex Bingham distribution; Hermitian matrix