Approximations for Three Statistical Functions

Statistical work connected with the computerized adaptive testing version of the Armed Services Vocational Aptitude Battery often involves the density and cumulative functions of the normal distribution, and the logistic function. In long, iterative calculations, computation of these functions can be time consuming. This research memorandum presents piecewise linear and cubic approximations for the normal cumulative distribution function, the logistic function, and the normal density function. The approximations are as accurate as library functions, and much faster in computing speed.