Saddlepoint approximations
著者
書誌事項
Saddlepoint approximations
（Oxford statistical science series, 16）（Oxford science publications）
Clarendon Press , Oxford University Press, 1995
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注記
Includes bibliographical references (p. [317]-325) and indexes
内容説明・目次
内容説明
Although introduced more than 60 years ago it is only during the last 15 years that there has been a systematic development of saddlepoint approximations. These approximations give a highly accurate expression for the tail of a distribution, not only in the centre of the distribution but also for very small tail probabilities. The price for this is a more cumbersome formula, the evaluation of which sometimes requires the use of a small personal computer. This book
explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of the subject. The emphasis is two- fold. One is on popularizing the formulae through many worked out and ready to use examples. The second is on giving a comprehensive mathematical
background for further research in the field. Some of the major subjects treated are uniformity of the approximations, tests in exponential families, and compound sums with applications in insurance mathematics.
目次
- 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
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