Comparison of algorithms for bivariate normal probability over a rectangle based on self-validated results from interval analysis ∗

Comparison of algorithms for computing probabilities and percentiles is often carried out in an effort to identify the best algorithm for various applications. One requirement when conducting comparative studies is some useable source of “satisfactory approximations to correct answers” to use as a basis when making accuracy comparisons. This paper reports success in applying elements of interval analysis to obtain a self-validating computational method for Bivariate Normal Probabilities. Results from applying this method can be used to provide a basis for accuracy studies of algorithms for Bivariate Normal probabilities. A study to compare several methods for computing probabilities over rectangles for this probability distribution, using the self-validated bases values, was carried out. The paper reports a choice of best method.