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 may require the use of a personal computer.
This text explains the ideas behind the saddlepoint approximations
as well as giving a detailed mathematical description of the
subject. The emphasis of the book 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 subjects
treated are uniformity of the approximations, tests in exponential
families and compound sums with applications in insurance
mathematics. This book is intended for researchers and graduate
students in statistics and consulting statisticians.
General
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