Von Neumann's Comparison Method for Random Sampling from the Normal and Other Distributions

Abstract

The author presents a generalization he worked out in 1950 of von Neumann's method of generating random samples from the exponential distribution by comparisons of uniform random numbers on (0,1). It is shown how to generate samples from any distribution whose probability density function is piecewise both absolutely continuous and monotonic on (negative infinity, infinity). A special case delivers normal deviates at an average cost of only 4.036 uniform deviates each. This seems more efficient than the Center-Tail method of Dieter and Ahrens, which uses a related, but different, method of generalizing the von Neumann idea to the normal distribution.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1972
Accession Number
AD0740330

Entities

People

  • George E. Forsythe

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Computer Science
  • Computers
  • Differential Equations
  • Distribution Functions
  • Equations
  • Intervals
  • Linear Differential Equations
  • Monte Carlo Method
  • Normal Distribution
  • Numerical Analysis
  • Probability
  • Probability Density Functions
  • Random Variables
  • Sampling
  • Statistical Samples
  • Statistical Sampling

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Statistical inference.