E(X) Logarithms, and the Normal Distribution

Abstract

The occurrence of e, the natural logarithm base, in widely used probability density functions, necessitates having elementary computer algorithms to evaluate numbers N represented N=e 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 one's intuition, logically compelling, and parsimonious. Keywords: Statistical models.

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Document Details

Document Type
Technical Report
Publication Date
Feb 19, 1988
Accession Number
ADA196044

Entities

People

  • Dallas R. Hodgins

Organizations

  • Naval Health Research Center

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computer Programming
  • Computer Programs
  • Computers
  • Distribution Functions
  • Health Care
  • Information Science
  • Integrals
  • Language
  • Normal Distribution
  • Numerical Analysis
  • Probability
  • Probability Density Functions
  • Programming Languages
  • Random Variables
  • Statistics

Readers

  • Calculus or Mathematical Analysis
  • Computational Linguistics
  • Computational Modeling and Simulation