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

• Author(s) / Creator(s)

  • Safouhi, Hassan
  • Gaudreau, Philippe J.
  • Slevinsky, Richard M.

• 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

  2012

• Subjects / Keywords

  • Extrapolation methods
  • Slevinsky–Safouhi formulae
  • Tails of probability distributions
  • G transformation
  • Rational and Pad´e approximants

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/R32S0D

• License

  © 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.