A representation in beta series for the exact density of some random volume contents |
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Authors: | Giorgio Pederzoli |
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Institution: | Concordia University , Montreal, Canada |
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Abstract: | Consider r independent and identically distributed random points in a unit n-ball of which p are in the interior and rp are on the surface. These r points, via their convex hull, generate an r-simplex. This article deals with the exact density of the r-content when the points are uniformly distributed. The exact density of the r-content is obtained for the general values of the parameters r, n and p. A representation of the density is given as a mixture of beta type-1 densities so that one can evaluate various types of probabilities by using incom-plete beta tables. |
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Keywords: | mixture representations of the exact density computable beta series |
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