Uniform saddlepoint approximations
- 1 September 1988
- journal article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 20 (3) , 622-634
- https://doi.org/10.2307/1427038
Abstract
The validity of the saddlepoint expansion evaluated at the pointyis considered in the limitytending to ∞. This is done for the expansions of the density and of the tail probability of the meanofni.i.d. random variables and also for the expansion of the tail probability of a compound Poisson sum, whereNis a Poisson random variable. We consider both general conditions that ensure the validity of the expansions and study the four classes of densities forX1introduced in Daniels (1954).Keywords
This publication has 11 references indexed in Scilit:
- Tail Probability ApproximationsInternational Statistical Review, 1987
- Approximations for compound Poisson and Pólya processesAdvances in Applied Probability, 1985
- Saddlepoint Approximations for Permutation Tests and Confidence IntervalsJournal of the Royal Statistical Society Series B: Statistical Methodology, 1982
- Saddle point approximation for the distribution of the sum of independent random variablesAdvances in Applied Probability, 1980
- A unified formulation of the central limit theorem for small and large deviations from the meanProbability Theory and Related Fields, 1979
- Edgeworth and saddlepoint approximations in the first-order noncircular autoregressionBiometrika, 1978
- Econometric Estimators and the Edgeworth ApproximationEconometrica, 1976
- Uniform asymptotic expansions of integrals with stationary point near algebraic singularityCommunications on Pure and Applied Mathematics, 1966
- On Deviations of the Sample MeanThe Annals of Mathematical Statistics, 1960
- Saddlepoint Approximations in StatisticsThe Annals of Mathematical Statistics, 1954