Inequalities for Propability Contents of Convex Sets via Geometric Average.
ARIZONA UNIV TUCSON
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This paper derives such an inequality for a large class of density functions and a large class fo convex sets. The most general results are given for the bivariate case. An extention to the n-dimensional case appears to be difficult except for some special cases such as the case of independent identically distributed random variables or when the underlying joint density is spherically symmetric. The class of convex sets considered includes D sub infinity and D sub 2 as special cases and special applications are given for elliptically contoured distributions and scale parameters families. In all these cases, universal upper bounds on the probability contents can be given by substituting the values of the a sub is by their geometric mean.
- Statistics and Probability