Geometric-vs-Arithmetic Averaging of Positive Random Variables.

Abstract

Many comparisons have shown that when acoustic data are analyzed by different processing systems, there are significant variations in the calculated values of sound pressure levels. Since the Naval Underwater Systems Center is engaged in making reliable underwater radiated noise measurements, the Center is interested in quantitative as well as qualitative explanations for these differences. The variations are due in part to the diverse methods used for data averaging. This report is the first of a series of reports dealing with the averaging of discrete and continuous data. In this report, the geometric mean is defined for a positive random variable, and methods are derived for computing the geometric mean. A quantity R is also defined which expresses the relative difference between geometric and arithmetic averaging. Examples are then presented to illustrate the application of the derived methods, and to indicate the difference between the geometric and arithmetic averages of several well-known probability distributions. (Author)

Document Details

Document Type
Technical Report
Publication Date
May 03, 1973
Accession Number
AD0910312

Entities

People

  • Dean J. Schmidlin

Organizations

  • Naval Underwater Systems Center

Tags

DTIC Thesaurus Topics

  • Arithmetic
  • Mathematics
  • Measurement
  • Noise
  • Pressure Distribution
  • Probability
  • Probability Distributions
  • Radiated Noise
  • Random Variables
  • Sound Pressure

Readers

  • Acoustical Oceanography.
  • Approximation Theory.
  • Team-Based Human-Centered Cognitive Task Decision Making and Information Performance.