SADDLEPOINT APPROXIMATION FOR THE DISTRIBUTION FUNCTION NEAR THE MEAN

BO YANG^{1} AND JOHN E. KOLASSA^{2}

1Department of Biostatistics, Shering–Plough Research Institute, 2000 Galloping Hill Road,

Kenilworth, NJ 07033-0530, U.S.A.

2Department of Biostatistics, University of Rochester, Box 630, Rochester, NY 14642, U.S.A.

(Received July 3, 2001; revised March 19, 2002)

Abstract. We repair numerical difficulties in applying saddlepoint tail probability approximations when the ordinate at which the approximation is evaluated is near the mean of the distribution approximated. These modifications apply to double saddlepoint approximations to conditional distributions as well.

Key words and phrases: Saddlepoint approximation, singularity.