Chebyshev subinterval polynomial approximations for continuous distribution functions

Abstract

An algorithm for constructing a three-subinterval approximation for any continous distribution function is presented in which the Chebyshev criterion is used, or equivalently, the maximum absolute error (MAE) is minimized. The resulting approximation of this algorithm for the standard normal distribution function provides a guideline for constructing the simple approximation formulas proposed by Shah [13]. Furthermore, the above algorithm is extended to more accurate computer applications, by constructing a four-polynomial approximation for a distribution function. The resulting approximation for the standard normal distribution function is at least as accurate as, faster, and more efficient than the six-polynomial approximation proposed by Milton and Hotchkiss [11] and modified by Milton [10].