Advances and Applications in Statistics
Volume 43, Issue 1, Pages 21 - 36
(November 2014)
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A TRIVARIATE BETA DISTRIBUTION AND RELATED DISTANCES
David P. Chu and Ali Reza Fotouhi
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Abstract: In this paper, we consider a trivariate beta distribution and give its probability density function explicitly as an infinite series. The joint moment of this distribution is expressed as an infinite series of beta functions, which is useful for numerical computations. The general case of a multivariate beta distribution, in terms of an infinite series, is also given. We compute the expected distance between two independent trivariate beta distributed random points in two cubic spaces as well as in one cubic space. Simulations are conducted for comparisons. The integer moments of the distance in a cube are given as well. |
Keywords and phrases: trivariate beta random points, expected distances, infinite series, moments, cubes. |
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