ABSTRACT
There has been a large amount of research conducted into methods for approximating probability functions, and there is a substantial amount of literature on this subject contained in many different periodicals. Reviewing this area of statistical computing is difficult because a multitude of different numerical methods are employed, often in differing forms, to construct algorithms. Successive applications of composite quadrature are often used to obtain an indication of the amount of error in approximation. Programming the Romberg integration method is not a difficult task. The primary considerations are efficiency and stopping criteria. Most mathematical subprogram libraries contain programs which provide values of the error function and its complement essentially to machine precision. The inverse error function is more difficult to approximate to machine precision than is the error function itself, so not all mathematical function program libraries contain this function.
