Sampling from the Multinomial Distribution on a Computer.

Abstract

This paper describes algorithms to effect multinomial sampling on a computer in ways that protect the sampler against an excess computing cost per sample. Section 2 presents the multinomial model together with an equivalent representation in terms of a series of binomial sampling experiments. The binomial representation is further discussed in Section 4. Sections 3 and 5 demonstrate the danger of using too simplistic a sampling scheme if execution time is a concern. Section 6 describes how a normal approximation to the binomial distribution can make execution time virtually independent of n. A criterion of acceptability is described. Section 7 describes an acceptance-rejection technique that, when used with a Poisson sample, allows the desired binomial sampling exactly. Using a normal approximation to the Poisson distribution, one can again generate multinomial samples virtually independent of n. Section 8 describes a procedure for binomial sampling based on the inverse transform method. Section 9 describes the ordering of the serial binomial experiments in response to alternative objectives. Section 10 describes algorithm M3 which puts all the suggestions of earlier sections together.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1978
Accession Number
ADA061651

Entities

People

  • George S. Fishman

Organizations

  • University of North Carolina at Chapel Hill

Tags

DTIC Thesaurus Topics

  • Acceptability
  • Algorithms
  • Binomials
  • Computer Programs
  • Computers
  • Military Research
  • Models
  • North Carolina
  • Numbers
  • Operations Research
  • Probability
  • Random Variables
  • Sampling
  • Simulations
  • Square Roots
  • Statistical Sampling

Fields of Study

  • Mathematics

Readers

  • Computational Modeling and Simulation
  • Mathematical Modeling and Probability Theory.
  • Molecular Photonics/Laser Physics