Operating Characteristics of Log-Normalizer for Weibull and Log-Normal Inputs.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 17, 1987
- Accession Number
- ADA188303
Entities
People
- Albert H. Nuttall
Organizations
- Naval Underwater Systems Center