A note on computing extreme tail probabilities of the noncentral t-distribution with large noncentrality parameter. The noncentral t-distribution is a generalization of the Student’st-distribution. In this paper we suggest an alternative approach for computing the cumulative distribution function (CDF) of the noncentralt-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 δ and the degrees of freedom ν. The implementation of the algorithm is available at the MATLAB Central [http://www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw].
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- Witkovský, Viktor: A note on computing extreme tail probabilities of the noncentral $t$-distribution with large noncentrality parameter (2013)