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Two phenomenological models are considered by which impulsive random noises can be described: (a) Poisson noise, consisting of the superposition of independent, randomly occurring elementary impulses. Much electronic noise belongs to this type and the familiar physical examples are precipitation noise, ignition noise, and solar ``static.'' (b) Poisson‐Poisson noise, consisting of the superposition of independent, randomly occurring Poisson noise, each type of Poisson noise forming a wave packet of some duration. Atmospheric noise is a representative example of the latter type. The attempt at first is made to deduce the general amplitude distribution for each model; then, because the noise sources in nature are spatially distributed and noise strength decreases with distance so that the amplitude of the received noise sometimes depends seriously on this spatial distribution of noise sources, the amplitude probability distributions are considered according to the two typical cases of the discrete and continuous spatial distributions, and are compared with those of actual atmospherics. Moments of even order and correlation functions are also calculated for each model. Finally, the dependence of the assumptions used on amplitude probability distribution are discussed. The distributions obtained are, in some cases, found to be independent of the adopted models and some of the used assumptions in a wide range of noise amplitude.