
Accession Number : ADA188303
Title : Operating Characteristics of LogNormalizer for Weibull and LogNormal 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 lognormalizer, subject to either lognormal 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 1E6. The receiver operating characteristics vary over the range of (P sub F, P sub D) equal to (1E6, 1E6) 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