Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators

Gatto, Riccardo; Peeters, Chantal (2015). Saddlepoint approximations to sensitivities of tail probabilities of random sums and comparisons with Monte Carlo estimators. Journal of statistical computation and simulation, 85(4), pp. 641-659. Taylor & Francis 10.1080/00949655.2013.834058

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This article proposes computing sensitivities of upper tail probabilities of random sums by the saddlepoint approximation. The considered sensitivity is the derivative of the upper tail probability with respect to the parameter of the summation index distribution. Random sums with Poisson or Geometric distributed summation indices and Gamma or Weibull distributed summands are considered. The score method with importance sampling is considered as an alternative approximation. Numerical studies show that the saddlepoint approximation and the method of score with importance sampling are very accurate. But the saddlepoint approximation is substantially faster than the score method with importance sampling. Thus, the suggested saddlepoint approximation can be conveniently used in various scientific problems.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Gatto, Riccardo

Subjects:

500 Science > 510 Mathematics

ISSN:

0094-9655

Publisher:

Taylor & Francis

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

19 Dec 2014 11:22

Last Modified:

07 Aug 2015 16:34

Publisher DOI:

10.1080/00949655.2013.834058

Uncontrolled Keywords:

change of measure, exponential tilt, Gamma distribution, geometric distribution, importance sampling, Poisson distribution, rare event, score Monte Carlo method, Weibull distribution, 41A60, 65C05

BORIS DOI:

10.7892/boris.60983

URI:

https://boris.unibe.ch/id/eprint/60983

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