Some exact distributions in traffic noise theory

Abstract

The moment-generating function of the traffic noise from a stream of vehicles with identical noise emissions cannot be readily inverted. If the emissions are not equal, this generating function can be inverted to obtain the exact form of the distribution function in some particular cases. Noise intensity has a maximally skew stable distribution with exponent 1/2 for observers on the highway, whatever the distribution of emissions. The distribution at any distance from the highway is an exponentially modified stable law with exponent 1/2 for an improper exponential distribution of emissions, and an infinite series involving this stable law and iterated error functions when emissions have an exponential distribution. A doubly stochastic process for emissions produces distributions of traffic noise intensity in the domain of attraction of skew stable laws with exponent α, 1/2 < α < 2. The inverse Gaussian (exponentially modified skew stable law with exponent 1/2) is recommended as the best choice of a two-parameter family for fitting traffic noise intensity distributions.