Bounds for distribution functions of sums of squares and radial errors
Bounds are found for the distribution function of the sum of squares X2+Y2 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 expre...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1991-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171291000765 |
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| Summary: | Bounds are found for the distribution function of the sum of squares X2+Y2 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 (X2+Y2)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. |
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| ISSN: | 0161-1712 1687-0425 |