## 1 Introduction  
It is well known that the parameters of natural waveguides (ocean, atmosphere), as well as optical, electrodynamic, plasma, dielectric, and other waveguides, to one degree or another, are subject to random variations [1; 2]. For example, during the propagation of an acoustic signal in the sea, one of the general sources of fluctuations of the main parameter, that is the speed of sound, is the passage of internal gravity waves (IGW) [3; 4; 5]. This circumstance is especially significant in the coastal (shelf) zones of the ocean, where a shallow water waveguide with a thermocline in the water column and a penetrable, absorbing bottom occurs for a low-frequency sound signal. As a rule, weak random perturbations of the speed of sound in such a waveguide cause a field of diffuse (background) internal waves that form on the \"tails\" of numerous collapses of nonlinear internal waves (solitons) when the latter passes into the shallow part of the sea shelf from the deepwater region [6]. Traditionally, on the basis of the central limit theorem, it is assumed that background internal waves lead to Gaussian perturbations of the sound speed in the sea. So, the influence of such fluctuations of the sound speed on the propagation of an acoustic signal in an oceanic waveguide has been studied for the past 40 years in numerous studies on this subject [7; 8; 9; 10], both theoretically and experimentally. Modern ideas about the effect of random inhomogeneities of the marine environment on the sound fields are based on the results of an approximate theory described in [7; 8; 9], as applied to the description of weak perturbations in the sound speed in the deep ocean when the internal waves travel with a special type of spectrum (Garrett-Munk spectrum). Subsequent attempts to transfer this theory, called the diffusion approximation, to sound propagation in the shelf zones of the ocean [11; 12; 13; 14; 18; 19; 20; 21; 22; 23; 24; 25; 26] showed that the theory poorly describes the situation if there are not fluctuations that are too weak, not small losses in the medium, but actual and also at typical distances for the shallow sea, not exceeding 50-100 km. There is nothing surprising in the fact that for the conditions of sound propagation in the shallow sea, fundamentally different than in the deep ocean, it became necessary to make adjustments to the previous theory in order to find out new statistical patterns. The first steps in this direction were made in [11; 21], where for weak fluctuations of the sound speed, in particular, strong fluctuations of the sound field were established at relatively small distances from the source and unusual changes were found in the law of decay of the field average intensity. We emphasize that new results are inherent in shallow water areas, where the bottom effect is significant. In the deep ocean, where acoustic waves propagate within the underwater sound channel, such patterns are not registered [9; 10; 15; 16; 17]. This paper briefly presents the previously obtained results of solving a two-dimensionally inhomogeneous statistical problem of sound propagation in a fluctuating shallow water waveguide with horizontal boundaries [21; 22; 23; 24; 25; 26]. Further, on the basis of the developed approach, examples of non-Gaussian probability distributions of sound velocity fluctuations are considered, and for these cases the results of a statistical simulation of the average intensity of a low-frequency acoustic signal are presented. A comparative analysis showed that the conclusions obtained for Gaussian fluctuations of the speed of sound are also valid for the considered examples with non-Gaussian fluctuations. Moreover, non-Gaussian fluctuations may even somewhat enhance the previously established effects of attenuation of the decay of the average signal intensity in the waveguide.