Saddlepoint Approximations [Hardcover]

During the last 15 years, there has been a systematic development of saddlepoint approximations. They give a highly accurate expression for the tail of a distribution, not only in the center but also for very small tail probabilities. Saddlepoint Approximations provides a complete account of this systematic development, giving worked out examples and comprehensive mathematical techniques for further research in the field. It will be most useful to researchers, students in statistics, and consulting statisticians.

1. Basic notions
2. Saddlepoint approximations for i.i.d. sums
3. Asymptotic expansions of integrals
4. Transformations of the basic approximation
5. Tests in exponential families
6. Uniform saddlepoint approximations
7. Compound sums
8. Alternative approximations
9. Markov chains
10. Non-standard situations
Appendix: Algorithms
List of symbols
References