Compound variance gamma distribution for randomly scattered sound and noise at multiple sensors

Gamma distributions for signal intensity (or, equivalently, Nakagami distributions for signal amplitude) are often used in acoustics and electromagnetics to describe the single-point statistics of randomly scattered signals and noise in urban and other complex environments. An extension of the gamma distribution, called the compound gamma (CG), has been furthermore shown [D. K. Wilson, M. J. Kamrath, C. E. Haedrich, D. J. Breton, and C. R. Hart, “Urban noise distributions and the influence of geometric spreading on skewness,” J. Acoust. Soc. Am. 150(2), 783–800 (2021)] to usefully generalize the gamma to scenarios in which the distribution becomes skewed due to random variations in the scattering strength or loudness of the noise sources. Here we present the compound variance gamma (CVG), which further generalizes the compound gamma to two-point statistics and is, therefore, useful for representing statistics on arrays of sensors or networks. The CVG distribution, which is expressed with a Gauss hypergeometric function, is shown to be in excellent agreement with realistic simulations of sound scattering in the atmosphere.