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Biometrika 1995 82(1):226-231; doi:10.1093/biomet/82.1.226
© 1995 by Biometrika Trust
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MISCELLANEA

Saddlepoint approximations for the difference of order statistics

JANE L. HARVILL1 and H. JOSEPH NEWTON2

1Department of Applied Statistics and Operations Research, Bowling Green State University Bowling Green, Ohio 43403-0267, U.S.A.
2Department of Statistics, Texas A&M University College Station, Texas 77843-3143, U.S.A.

Saddlepoint approximations for the distribution of the difference of order statistics from a continuous distribution are presented. The approximations are illustrated for the case of the exponential distribution where we can find the exact probability density function of the difference of order statistics, and for the case of the noncentral chi-squared distribution which has application to the problem of testing a time series for linearity. In both cases we show that the saddlepoint approximation is much better than the normal approximation, especially for realistic sample sizes.

Key Words: Interquartile range • Noncentral chi-squared • Nonlinear time series • Order statistic • Saddlepoint approximation


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