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Evaluating Parametric Probability Density Functions for Urban Acoustic Noise

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Technical Report

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Engineer Research and Development Center (U.S.) Hanover United States

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This paper evaluates the suitability of three parametric probability density functions for characterizing urban acoustic noise. For that purpose, the sound levels in one-third-octave bands 6.3 Hz-20 kHz were measured every 0.5 seconds for 5 minutes for a total of 600 measurements at 38 locations in Boston, USA. The probability density functions for this dataset were approximated using histograms and the log-normal, generalized gamma, and compound gamma distributions. Maximizing the log-likelihood for each distribution yielded their parameters. The suitability of each distribution was evaluated using the Kullback-Leibler divergence with the histogram approximation as the reference. Overall, the compound gamma distribution was the most accurate followed by the log-normal and then the generalized gamma distributions. Nonetheless, the simplicity of the two-parameter log-normal distribution might be preferred over the three-parameter compound gamma distribution in some applications. For the compound gamma distribution, the distributions of its parameters across all locations and frequencies were also approximated parametrically, which provided satisfactory agreement.

Subject Categories:

  • Acoustics
  • Statistics and Probability

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