In this paper a novel method for informative frequency band selection is presented. It is suitable for a vibration signal from a damaged rotating machine which is consisted of a pulse train, but it might be contaminated by other vibrations, often with higher energy. We first decompose the signal into simpler sub-signals and analyze those sub-signals using statistical tools, i.e. autoregressive moving average modelling and fitting of the α -stable distribution. The choice of this distribution is motivated by its excellent ability of modeling heavy-tailed data, i.e impulsive data. We illustrate the proposed methodology by analysis of real vibration signals from heavy-duty rotating machinery. The results prove that this statistical analysis is very efficient in informative frequency band selection in presence of high-energy contamination