Bounds for distribution functions of sums of squares and radial errors

Roger B. Nelsen and Berthold Schweizer

International Journal of Mathematics and Mathematical Sciences, 1991, vol. 14, 1-9

Abstract:

Bounds are found for the distribution function of the sum of squares X 2 + Y 2 where X and Y are arbitrary continuous random variables. The techniques employed, which utilize copulas and their properties, show that the bounds are pointwise best-possible when X and Y are symmetric about 0 and yield expressions which can be evaluated explicitly when X and Y have a common distribution function which is concave on ( 0 , ∞ ) . Similar results are obtained for the radial error ( X 2 + Y 2 ) ½ . The important case where X and Y are normally distributed is discussed, and here best-possible bounds on the circular probable error are also obtained.

Date: 1991
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:292756

DOI: 10.1155/S0161171291000765

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