Error Statistics for Normal Random Variables

Abstract

Four commonly used error statistics (the root mean square error, the geometric mean error, the mean radial error, and the spherical (or circular) error probable) are surveyed and compared in two and three dimensions. Exact or approximate closed-form expressions are given for these statistics for zero- mean, independent, normal random variables. A change of variables reduces the case of correlated variables to the independent case. The expression for the mean radial error in three dimensions and the approximations of the spherical error probable are new. The dependence of the statistics on the variances of the errors is presented graphically.

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Document Details

Document Type
Technical Report
Publication Date
May 07, 1975
Accession Number
ADA011430

Entities

People

  • Denis M. Coffey
  • Donald R. Childs
  • Stephen P. Travis

Organizations

  • Naval Undersea Warfare Center

Tags

Communities of Interest

  • Air Platforms
  • Weapons Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Circular Error Probable
  • Classification
  • Computer Programming
  • Covariance
  • Data Science
  • Distribution Functions
  • Equations
  • Errors
  • Information Science
  • Normal Distribution
  • Probability
  • Probability Distributions
  • Random Variables
  • Statistics
  • Test And Evaluation
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Regression Analysis.