Computing the noncentral beta distribution with S-system. (Q1575397)

Based on the recasting techniques of \textit{P. F. Rust} and \textit{E. O. Voit} [J. Stat. Computat. Simulation 42, No. 3--4, 187--249 (1992); Biom J. 32, 681--695 (1990; Zbl 0716.62027); J. Am. Stat. Assoc. 85, 572--578 (1990)], an S-system form of the noncentral beta distribution is extended from that of the noncentral F distribution and the other one is newly derived. The computing methods of this distribution have received much attention during the last decade. Its cumulative probabilities, densities, quantiles and related distributional values can be calculated in one \(S\)-system form. We demonstrate the new computational results using the \(S\)-system numerical solver ESSYNS. Consistent results are obtained from these two \(S\)-system forms under various situations. In addition, we compare the performance with an ad hoc computing method by evaluating the cumulative probabilities and densities jointly. The S-system formulation provides significant numerical advantages over its original form. Further properties are also discussed.