Short-term forecasts of air pollution levels in big cities are now reported in news-papers and other media outlets. Studies indicate that even short-term exposure to high levels of an air pollutant called atmospheric particulate matter can lead to long-term health effects. Data are typically...

Suppose thatX~N-m([mu], [Sigma], [Theta]). An expression for the density function is given when[Sigma][greater-or-equal, slanted]0 and/or[Theta]:[greater-or-equal, slanted]0. An extension of Uhlig's result (Uhlig [17]) is expanded for the singular value decomposition of a matrixZof...

Short-term forecasts of air pollution levels in big cities are now reported in news-papers and other media outlets. Studies indicate that even short-term exposure to high levels of an air pollutant called atmospheric particulate matter can lead to long-term health effects. Data are typically...

In shape analysis, it is usually assumed that the matrix X:N-K of the co-ordinates of landmarks in K is isotropic Gaussian. Let Y:(N-1)-K be the centered matrix of landmarks from X so that Y ~ N([mu], [sigma]2I). Let Y=TT be the Bartlett decomposition of Y into lower triangular, T, and...

Motivated by examples in protein bioinformatics, we study a mixture model of multivariate angular distributions. The distribution treated here (multivariate sine distribution) is a multivariate extension of the well-known von Mises distribution on the circle. The density of the sine distribution...