SADDLEPOINT APPROXIMATIONS FOR THE DIFFERENCE OF ORDER-STATISTICS

Saddlepoint approximations for the distribution of the difference of o rder statistics from a continuous distribution are presented. The appr oximations are illustrated for the case of the exponential distributio n where we can find the exact probability density function of the diff erence of order statistics, and for the case of the noncentral chi-squ ared distribution which has application to the problem of testing a ti me series for linearity. In both cases we show that the saddlepoint ap proximation is much better than the normal approximation, especially f or realistic sample sizes.