A survey of statistical models for urban noise and their physical interpretations

Many different models have been used to describe statistical distributions of sound in urban environments. Some models may be justified empirically, whereas others are linked to physical phenomena such as random fading, multipath, multi-source mixtures, and variations in source-receiver geometries. This presentation reviews many of the available statistical distributions, what they are intended to represent physically, and their appearance on linear and logarithmic (decibel) axes. To evaluate the suitability of the various distributions, comparisons are made to an experiment in which one-third octave band sound-level data were measured at 37 locations in the North End of Boston, Massachusetts. Based on the Kullback-Leibler divergence as calculated across all the locations and frequencies, the exponentially modified Gaussian (EMG) distribution provides the most consistently good agreement with data, because it captures the positively skewed sound levels present in most of the data. The compound gamma distribution, which is applicable to situations involving varying sound levels, also fits the data well and even outperforms the EMG for the small minority of cases exhibiting negative skew. The log-normal distribution often provides a suitable fit in cases where particular non-traffic noise sources dominate.