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- W2057074711 abstract "The convex hull generated by p linearly independent points in Euclidean n -space, n ⩾ p will almost surely determine a p -simplex and the corresponding p -parallelotope. The volume of this p -parallelotope is v = | XX ′ | 1 2 where the rows of the p × n , n ⩾ p matrix of rank p represent the p linearly independent points. If the points are random points in some sense then v becomes a random volume. The distribution of this random volume v when the matrix X has a very general real rectangular matrix-variate density is the topic of this paper. The complicated classical procedures based on integral geometry techniques for dealing with such problems are replaced by a simpler procedure based on Jacobians of matrix transformations and functions of matrix argument. Apart from the distribution of v under this general model, arbitrary moments of v , connection to the likelihood ratio statistic or λ -criterion for testing hypotheses on the parameters of multivariate normal distributions, connections to Mellin–Barnes integrals and Meijer’s G-function, connection to the concept of generalized variance, various structural decompositions of v and special cases are also examined here." @default.
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- W2057074711 date "2007-08-01" @default.
- W2057074711 modified "2023-09-28" @default.
- W2057074711 title "Random volumes under a general matrix-variate model" @default.
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- W2057074711 doi "https://doi.org/10.1016/j.laa.2007.03.022" @default.
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