On certain random simplices in n

W. J. Anderson

Journal of Multivariate Analysis, 1986, vol. 19, issue 2, 265-272

Abstract: The exact density is given for the r-content of the simplicial convex hull of r + 1 independent points in n, each having a type II [beta] distribution. The density is given in the form of an integral of Mellin-Barnes type, which even in the most general cases can be evaluated to give a series representation for the density. Some special cases are evaluated to observe the types of series that can arise. It is also shown that the r-content is asymptotically normal for large values of n, a result analogous to a result conjectured by R. E. Miles (1971, Adv. in Appl. Probab., 3 353-382).

Keywords: Type; II; beta; distribution; geometric; probability; Mellin-Barnes; integral; exact; densities; asymptotic; normality (search for similar items in EconPapers)
Date: 1986
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