Saddlepoint Approximations for the Difference of Order Statistics and Studentized Sample Quantiles


Chunsheng Ma and John Robinson


Research Report 97-36 Date: December 1997


For a sample from a given distribution the difference of two order statistics and the studentized quantile are statistics whose distribution is needed to obtain tests and confidence intervals for quantiles and quantile differences. This paper gives saddlepoint approximations for densities and saddlepoint approximations of the Lugannani-Rice form for tail probabilities of these statistics. The relative errors of the approximations are 1/n uniformly in a neighbourhood of the parameters and this uniformity is global if the densities are log-concave.

Key phrases

saddlepoint approximation. Laplace method. difference of order statistics. Studentized sample quantile.

AMS Subject Classification (1991)

Primary: 62G09
Secondary: 62G15


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