An Approximation to the Probability Normal Distribution and its Inverse

Resumen

Mathematical functions are used to compute Normal probabilities, whichabsolute errors are small; however their large relative errors make them unsuitableto compute structural failure probabilities or to compute the menacecurves of natural hazards. In this work new mathematical functions are proposedto compute Normal probabilities and their inverses in an easy andaccurate way. These functions are valid over a wide range of random variableand are useful in applications where computational speed and efficiencyare required. In addition, these functions have the advantage that the numericalcorrespondence between the random value X = x and its Normal probabilityΦ (-x) is bijective.