Selecting a parametric probability density function for urban sound

Abstract

In an urban setting, sound levels vary over time and space due to transportation, construction, and other community noise sources. Parametric probability density functions (PDFs) can concisely characterize these variations, but the literature does not identify an appropriate PDF that both has a firm theoretical foundation and fits urban sound data well. A Gaussian distribution, which physically corresponds to a single dominant source, sometimes describes a distribution of levels well, but often it does not. Frequently, the distribution falls somewhere between the idealizations of a single dominant source and many comparable sources, so a model that can approximate both cases could perform better than a Gaussian distribution. To that end, this presentation considers the generalized gamma and compound gamma distributions for modeling the normalized mean squared pressure. Creating histograms of acoustic data, which were collected in Boston, provides a basis to compare the distributions using the Kullback-Leibler (KL) divergence. In general, compared to the generalized gamma and log-normal distributions, the compound gamma distribution has a lower KL divergence and thus more closely matches the experimental distributions.