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False alarms in active sonar systems arising from physical objects in the ocean (e.g., rocks, fish, or seaweed) are often called clutter. A variety of statistical models have been proposed for representing the sonar probability of false alarm (Pfa) in the presence of clutter, including the log-normal, generalized-Pareto, Weibull, and K distributions. However, owing to the potential sparseness of the clutter echoes within the analysis window, a mixture distribution comprising one of the clutter distributions and a Rayleigh-distributed envelope (i.e., an exponentially distributed intensity) to represent diffuse background scattering and noise is proposed. Parameter-estimation techniques based on the expectation-maximization (EM) algorithm are developed for mixtures containing the aforementioned clutter distributions. While the standard EM algorithm handles the mixture containing log-normal clutter, the EM-gradient algorithm, which combines the EM algorithm with a one-step Newton optimization, is necessary for the generalized-Pareto and Weibull cases. The mixture containing K -distributed clutter requires development of a variant of the EM algorithm exploiting method-of-moments parameter estimation. Evaluation of three midfrequency active-sonar data examples, spanning mildly to very heavy-tailed Pfa, illustrates that the mixture models provide a better fit than single-component models. As might be expected, inference on clutter-source scattering based on the shape parameter of the clutter distribution is shown to be less biased using the mixture model compared with a single-component distribution when the data contain both clutter echoes and diffuse background scattering or noise.