PROBABILITY DENSITY FUNCTIONS OF n VECTORS ADDED WITH RANDOM DIRECTIONS.

Abstract

The probability density function of the resultant amplitude of n vectors in two dimensions, added with random directions, was calculated through an integral transformation which takes a probability density function for k components into a probability density function for k + 1 components. Examples were calculated to show the qualitative aspects of the density functions for 2, 3, and 4 components, with arbitrarily given magnitudes. For n = or > 5, the probability distribution rapidly approaches the Rayleigh distribution. The method also allows the use of a Rayleigh vector as one of the components. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jul 17, 1969
Accession Number
AD0691770

Entities

People

  • Edward L. Wright

Organizations

  • United States Naval Research Laboratory

Tags

DTIC Thesaurus Topics

  • Amplitude
  • Data Science
  • Information Science
  • Integrals
  • Mathematics
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables

Readers

  • Fluid Dynamics.
  • Regression Analysis.