Very small tails of the t distribution, and significance tests for clustering
Journal of Statistical Computation and Simulation
A new method for approximating improper integrals
SIAM Journal on Numerical Analysis
Computation of the Noncentral Gamma Distribution
SIAM Journal on Scientific Computing
Modern Engineering Statistics
Practical Extrapolation Methods: Theory and Applications
Practical Extrapolation Methods: Theory and Applications
New formulae for higher order derivatives and applications
Journal of Computational and Applied Mathematics
Extended procedures for extrapolation to the limit
Journal of Computational and Applied Mathematics
Extensions of Drummond's process for convergence acceleration
Applied Numerical Mathematics
Applied Numerical Mathematics
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We use the recently developed algorithm for the $G_{n}^{(1)}$ 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 $G_{n}^{(1)}$ transformation required symbolic computation of large determinants. With the use of our algorithm, the $G_n^{(1)}$ transformation can be performed relatively easily to produce explicit approximations. After a brief theoretical study, a connection between the $G_n^{(1)}$ transformation and rational and Padé approximants is established.