computation of tail probability distributions via extrapolation methods and connection with rational and pade approximants

• DOI: 10.7939/r32s0d
• Publication Date: 2012-01-01
• Authors: Safouhi, Hassan; Gaudreau, Philipp...; Slevinsky, Richar...
• Keywords: Extrapolation methods; Tails of probability distributions; G transformation; Slevinsky–Safouhi formulae; Rational and Pad´e approximants; 0101 mathematics; 01 natural sciences

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.