In this paper, a mixture of generalized Cauchy distribution and Rayleigh distribution that possesses a closed-form\nexpression is proposed for modeling the heavy-tailed Rayleigh (HTR) distribution. This new approach is developed for\nanalytically modeling the amplitude distribution of ultrasound images based on the HTR distribution. HTR as a\nnon-Gaussian distribution is basically the amplitude probability density function (PDF) of the complex isotropic\nsymmetric �±-stable (S�±S) distribution which appears in the envelope distribution of ultrasonic images. Analytic\nexpression for HTR distribution is a momentous consideration in signal processing with stable random variables.\nFurthermore, we introduce a mixture ratio estimator based on the energy of amplitude PDF which contains both �±\nand �³ parameters. For a quantitative assessment, we compare the accuracy and computational complexity of the\nproposed mixture with other approximations of HTR distribution through several numeral simulations on synthetic\nrandom samples. Experimental results obtained from the Kolmogorov-Smirnov (K-S) distance and Kullback-Leibler\n(K-L) divergence as the goodness-of-fit tests on real ultrasound images reveal the favor of the new mixture model.
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