Comparing S-system with existing methods for the computation of noncentral beta distribution

Based on the recasting illustrations of Rust and Voit [13], we newly recast the noncentral beta distribution into the S-system form with numerical advantages. The computing methods of this distribution have received much attention during the last decade. They differ in various situations, for instance, error bound, the approximation or truncation method, the simplicity of representations, and the calculation procedure. Most of them focus on computing cumulative probabilities. The S-system formulation can further evaluate other quantities, such as density and quantiles, more easily and interactively. In addition to demonstrating the new computational results using the S-system numerical solver ESSYNS, we also compare the evaluation results with those by the ad hoc computing methods. Some numerical results and its comparisons are also shown.