The focus of this paper is on the prediction of the fatigue life of aircraft panels subjected to the combination of a strong random acoustic excitation and to steady thermal effects. More specifically, a novel parametric model for the probability density function of the ranges (displacement or stress) is proposed and is validated using a set of 44 time histories of displacement and stresses. These time histories correspond to the response of a single well Duffing oscillator, the displacements and stresses of a NASTRAN plate model that is either buckled or unbuckled and subjected to an acoustic excitation at either normal or grazing incidence. Finally, strain gauge data recorded during testing of an unbuckled panel at the Air Force Research Laboratory is also considered. The matching of the exact distribution of ranges and its model is at least very good in all 44 cases. Finally, the dependency of the 5 parameters of the model on the spectral moments of the response is clarified to enable a direct prediction of the fatigue life.