A uniform approximation to the right normal tail integral

摘要

This paper presents two simple formulas for approximation of the standard normal right tail probabilities, and indicates the method of computing approximations of higher order. One of the approximations relies on two simple numerical constants, has absolute error of 0.00071 and relative error 0.023; the other uses four numerical constants, has absolute error of 0.000019, the relative error is 0.005 and gives at least two significant digits for probabilities over the entire range 0⩽z<∞.