Bounds for distribution functions of sums of squares and radial errors
Abstract
Bounds are found for the distribution function of the sum of squaresX2+Y2whereXandYare arbitrary continuous random variables. The techniques employed, which utilize copulas and their properties, show that the bounds are pointwise best-possible whenXandYare symmetric about0and yield expressions which can be evaluated explicitly whenXandYhave a common distribution function which is concave on(0,∞). Similar results are obtained for the radial error(X2+Y2)½. The important case whereXandYare normally distributed is discussed, and here best-possible bounds on the circular probable error are also obtained.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 01, 1991
- Source ID
- 10.1155/s0161171291000765
Entities
People
- Berthold Schweizer
- Roger B. Nelsen
Organizations
- Lewis & Clark College
- Office of Naval Research
- University of Massachusetts