Saddlepoint Approximations for a Product and Its Application

Abstract

A technique of the saddlepoint approximation with double exponential base, SPA_D is developed to evaluate the probability of a product of two random variables, which may be independent or dependent, normal or contaminated normal random variables. The SPA_D shows a slightly better approximation as compared to the saddlepoint approximation with Lagannani–Rice formula. However, both methods get remarkable results when applied to evaluate the tail probabilities of the Reynolds stress for soil erosion prediction.

Keywords:

• Double-exponential distribution
• Probability of product
• Saddlepoint approximation

Mathematics Subject Classification:

• 65Cxx

Acknowledgment

This work was partially supported by National Science Council of the R.O.C. under grant NSC 94-2211-E-005-003.

Notes

r.err = |p − Exact|/(1 − Exact)*100%.