E(X) Logarithms, and the Normal Distribution

The occurrence of e, the natural logarithm base, in widely used probability density functions, necessitates having elementary computer algorithms to evaluate numbers N represented Ne sub x. Programs are presented that find x given N, find N given x, and use these operations in developing a rational approximation for the normal Gaussian probability density function integral. Accuracy of the order of three parts in ten million are assured in the logarithm routine. The exponential process is accurate to two parts in ten billion and the density function is in error by only one and one half units in the seventh decimal digit. The MUMPS Massachusetts General Hospital Utility Multi-Programming System string functions EXTRACT, FIND and LENGTH are shown to be efficient aids in examining numbers. MUMPS, numerical analysis, and compiler standards for number manipulation are briefly discussed. Fast, efficient numerical algorithms are realizable in the MUMPS environment. The string manipulation operators, in particular, allow concise and readable code. MUMPS is a vastly underrated programming language with respect to numerical analysis. It is appealing to ones intuition, logically compelling, and parsimonious. Keywords Statistical models.