Efective symbol detection, channel estimation and decoding of channel codes require an accurate characterization of the noise probability distribution. In many systems, notably the internet of things, noise is largely in the form of interference, arising from a massive number of simultaneous transmissions from uncoordinated devices. Obtaining the probability distribution of the interference is a challenging problem due to the use of non-orthogonal multiple access schemes over several subcarriers (leading to multivariate statistical models) and the heavy-tailed nature of the interference due to the random locations of devices. In this paper, we derive a novel tractable characterization of the interference probability distribution based on an application of Sklar’s theorem to develop a combination of α-stable and t-copula dependence models. We demonstrate that this formulation produces an accurate statistical modeling framework that admits efcient parameter estimation methods. As an illustration of the utility of our models, we develop a simple-to-implement nonlinear receiver when a binary signal is transmitted over all subcarriers by the desired transmitter, which is efective in a range of scenarios and can signifcantly outperform existing approaches.