This study investigate the statistics of a Sine on Random (SoR) process, defining the probability density function of the maximum values as well as the joint probability density function of the amplitude and the mean. The reasons for investigating SoR process are to be found in the wide use of SoR to recreate vibratory environments generated by machines with rotating parts (i.e. helicopters and propeller aircraft). The starting point of the study is the well-known Rice distribution, which describes an analytical solution in the hypothesis in which the random is narrow band and the sine falls within or close to this band. For this reason, the problem was tackled by looking for the solution outside Rice's hypotheses, identifying two domains: the first in which the pure tone has a lower frequency than the random, the second in which the situation is reversed. For each of these domains a solution has been proposed, then validated numerically and experimentally. The discussion trying to lay the foundations for the application of spectral methods to SoR type processes