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A note on computing extreme tail probabilities of the noncentral \(t\)-distribution with large noncentrality parameter. (English) Zbl 1302.62034
Summary: 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 [http://www.mathworks.com/matlabcentral/fileexchange/41790-nctcdfvw].
MSC:
62E15 Exact distribution theory in statistics
62-04 Software, source code, etc. for problems pertaining to statistics
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