%0 Generic %1 witkovsky2013computing %A Witkovsky, Viktor %D 2013 %K distributions t %T A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter %U http://arxiv.org/abs/1306.5294 %X 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.

@misc{witkovsky2013computing, 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.}, added-at = {2015-02-05T16:01:31.000+0100}, author = {Witkovsky, Viktor}, biburl = {https://www.bibsonomy.org/bibtex/29d7cfa3df0585e9354c6c1ae0dcd6864/shabbychef}, description = {A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter}, interhash = {2de31463ac7e4c3caafbde74ab3f0afb}, intrahash = {9d7cfa3df0585e9354c6c1ae0dcd6864}, keywords = {distributions t}, note = {cite arxiv:1306.5294Comment: Preprint submitted to Acta Universitatis Palackianae Olomucensis, Facultas rerum naturalium, Mathematica, submitted June 21, 2013, revised September 4, 2013}, timestamp = {2015-02-05T16:01:31.000+0100}, title = {A Note on Computing Extreme Tail Probabilities of the Noncentral T Distribution with Large Noncentrality Parameter}, url = {http://arxiv.org/abs/1306.5294}, year = 2013 }