Acoustic and ultrasonic propagation results in a Linear Invariant Filter (LIF). Its complex gain is most often described by a ‘frequency power law’. Equivalently, the complex gain is the characteristic function (c.f.) of a ‘stable probability law’. This strong property justifies a modelization by ‘random propagation times’, which together predict the measured attenuations and obey the principle of energy balance. Except for a Gaussian component, propagation through the atmosphere has no connection with ‘frequency power laws’. In this paper, we show that other components are c.f. of probability laws linked to Poisson and exponential random variables (r.v). Consequently, random propagation times are able to explain propagation losses in the atmosphere.