For evaluating the output response fluctuation of the actual environmental acoustic system excited by arbitrary random inputs, it is important to predict a whole probability distribution form closely connected with many noise evaluation indexes Lx, Leq and so on. In this paper, a new type evaluation method is proposed by introducing lower and higher order type functional models matched to the prediction of the response probability distribution form especially from a problem-oriented viewpoint. Because of the non-negative property of the sound intensity variable, the response probability density function can be reasonably expressed in advance theoretically by a statistical Laguerre expansion series form. The system characteristic between input and output can be described by the regression relationship between the distribution parameters (containing expansion coefficients of this expression) and the stochastic input. These regression functions can be expressed in terms of the orthogonal series expansion. Since, in the actual environment, the observed output is inevitably contaminated by the background noise, the above regression functions can not be directly employed as the models for the actual environment. Fortunately, the observed output can be given by the sum of the system output and the background noise on the basis of additivity of intensity quantity and the statistical moments of the background noise can be obtained in advance. So, the models relating the regression functions to the function of the observed output can be derived. Next, the parameters of the regression functions are determined based on the least-squares error criteria and the measure of statistical independency according to the level of non-Gaussian property of the function of the observed output. Thus, by using the regression functions obtained by the proposed identification method, the probability distribution of the output reducing the background noise can be predicted. Finally, the effectiveness of the proposed method is confirmed experimentally too by applying it to an actual indoor-outdoor acoustic system.