Computation of tail probability distributions via extrapolation methods and connection with rational and Padé approximants. Open Access


Author or creator
Gaudreau, Philippe J.
Slevinsky, Richard M.
Safouhi, Hassan
Additional contributors
tails of probability distributions
rational and Pad´e approximants
extrapolation methods
G transformation
Slevinsky–Safouhi formulae
Type of item
Journal Article (Published)
Abstract. We use the recently developed algorithm for the G(1) n transformation to approximate tail probabilities of the normal distribution, the gamma distribution, the student’s t-distribution, the inverse Gaussian distribution, and Fisher’s F distribution. Using this algorithm, which can be computed recursively when using symbolic programming languages, we are able to compute these integrals to high predetermined accuracies. Previous to this contribution, the evaluation of these tail probabilities using the G(1) n transformation required symbolic computation of large determinants. With the use of our algorithm, the G(1) n transformation can be performed relatively easily to produce explicit approximations. After a brief theoretical study, a connection between the G(1) n transformation and rational and Pad´e approximants is established.
Date created
License information
© 2012 Philippe J. Gaudreau et al. This version of this article is open access and can be downloaded and shared. The original author(s) and source must be cited.
Citation for previous publication
Gaudreau, P., Slevinsky, R., and Safouhi, H. (2012). Computation of tail probability distributions via extrapolation methods and connection with rational and Padé approximants.. SIAM Journal of Scientific Computing, 34(1), B65-B85.
Link to related item

File Details

Date Uploaded
Date Modified
Audit Status
Audits have not yet been run on this file.
File format: pdf (Portable Document Format)
Mime type: application/pdf
File size: 270913
Last modified: 2016:11:08 16:52:03-07:00
Filename: SJSC_34_1_2012_B65.pdf
Original checksum: 34bea6f5edccbceeada63ef7e42fb8ee
Well formed: false
Valid: false
Status message: java.lang.ClassCastException: edu.harvard.hul.ois.jhove.module.pdf.PdfSimpleObject cannot be cast to edu.harvard.hul.ois.jhove.module.pdf.PdfDictionary offset=269898
File title: Computation of Tail Probabilities via Extrapolation Methods and Connection with Rational and Pad Approximants
File author: Philippe Gaudreau, Richard M. Slevinsky, and Hassan Safouhi
Activity of users you follow
User Activity Date