Evaluating Parametric Probability Density Functions for Urban Acoustic Noise
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.
- Statistics and Probability