Numerical Evaluation of Integrals Involving the β‐PDF

The fast and accurate evaluation of expected values involving the probabilistic β‐distributions poses severe problems to standard numerical integration schemes. An efficient algorithm to evaluate such integrals is presented based on approximation and analytical evaluation rather than numerical integration. Starting from an extension of the 2‐parameter family of β‐distributions a criterion is derived to assess the correctness of any integration scheme in the numerically demanding limiting cases of this family.