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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 whereXandYaredoi:10.1155/s0161171291000765 fatcat:p63b43qehbeprgjpnvfvgra2ei