Accession Number : ADA188303

Title :   Operating Characteristics of Log-Normalizer for Weibull and Log-Normal Inputs.

Descriptive Note : Technical rept.,

Corporate Author : NAVAL UNDERWATER SYSTEMS CENTER NEW LONDON CT NEW LONDON LAB

Personal Author(s) : Nuttall, Albert H

PDF Url : ADA188303

Report Date : 17 Aug 1987

Pagination or Media Count : 94

Abstract : The false alarm and detection probabilities of a log-normalizer, subject to either log-normal or Weibull input statistics, are derived for general input signals and noise strengths and number of normalizer samples, N. Plots of the exceedance distribution function versus the threshold, as well as the receiver operating characteristics (i.e., detection probability P sub D vs. false alarm probability P sub F) are plotted for N = infinity, 64, 32, 16 and for various values of the normalizer input deflection statistic d. In addition, simulation results, based on 8.4 million trials, are super posed for purposes of confirming or rejecting the theoretical results. Plots of the exceedance distribution function are carried out on the extremes of the distribution, to the point where the tail probabilities are 1E-6. The receiver operating characteristics vary over the range of (P sub F, P sub D) equal to (1E-6, 1E-6) through (.5, .99). It is found that the theoretical analysis for the log normal input is exact for all N, whereas the approximate theoretical analysis for the Weibull input is sufficiently accurate only for large N, and not on the tails of the distribution. Keywords: False alarm probability, Log normal variates; Log normalizer; Normalized random variables, Operating characteristics, Sample mean; Sample standard deviation; Weibull variates; Constant false alarm rate; Deflection criterion; Detection probability; Exceedance distribution.

Descriptors :   *FALSE ALARMS, *TAIL ASSEMBLIES, *ACOUSTIC DETECTION, *SONAR, *STATISTICAL ANALYSIS, APPROXIMATION(MATHEMATICS), DETECTION, DISTRIBUTION FUNCTIONS, INPUT, NOISE, PROBABILITY, RANDOM VARIABLES, RATES, SIMULATION, STANDARD DEVIATION, STATISTICS, STRENGTH(GENERAL), THEORY, WEIBULL DENSITY FUNCTIONS, MEAN, GAUSSIAN NOISE

Subject Categories : Acoustic Detection and Detectors
      Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE