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noncentral $t$-distribution; cumulative distribution function (CDF); noncentrality parameter; extreme tail probability; MATLAB algorithm
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:
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