Geodesic
A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 131-143.

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The noncentral $t$-distribution is a generalization of the Student’s$t$-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentral$t$-distribution which is based on a direct numerical integration of a well behaved function. With a double-precision arithmetic, the algorithm provides highly precise and fast evaluation of the extreme tail probabilities of the noncentral $t$-distribution, even for large values of the noncentrality parameter $\delta $ and the degrees of freedom $\nu $. The implementation of the algorithm is available at the MATLAB Central, File Exchange: www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.
Classification : 62-04, 62E15
Keywords: noncentral $t$-distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm 
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Witkovský, Viktor. A Note on Computing Extreme Tail Probabilities of the Noncentral $t$-Distribution with Large Noncentrality Parameter. Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica, Tome 52 (2013) no. 2, pp. 131-143. http://geodesic.mathdoc.fr/item/AUPO_2013__52_2_a11/