Uniform Saddlepoint Approximations and Log-Concave Densities
Jens Ledet Jensen · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1991
SUMMARY For a one-dimensional variable with a log-concave density it is shown that the saddlepoint approximations to the density and the distribution function of the mean are uniformly valid. A double-saddlepoint approximation to a conditional distribution function is introduced, which is uniformly valid for a two-dimensional log-concave density. The results are illustrated with the log-normal distribution and the gamma distribution.