A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter

Abstract

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: http://www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw.

Preprint submitted to Acta Universitatis Palackianae Olomucensis, Facultas rerum naturalium, Mathematica, submitted June 21, 2013, revised September 4, 2013