Saddlepoint Approximations

Hardcover | April 30, 1999

byJens L. Jensen

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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 alsofor 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 thesubject. 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, testsin exponential families, and compound sums with applications in insurance mathematics.

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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 alsofor very small tail probabilities. The price...

Jens L. Jensen is at University of Aarhus.

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Format:HardcoverDimensions:344 pages, 9.21 × 6.14 × 0.94 inPublished:April 30, 1999Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198522959

ISBN - 13:9780198522959

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Table of Contents

1. Basic notions2. Saddlepoint approximations for i.i.d. sums3. Asymptotic expansions of integrals4. Transformations of the basic approximation5. Tests in exponential families6. Uniform saddlepoint approximations7. Compound sums8. Alternative approximations9. Markov chains10. Non-standard situationsAppendix: AlgorithmsList of symbolsReferences