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Purpose The study of speckle from imaging systems has a rich history, and recently it was proposed that a fractal or power law distribution of scatterers in vascularized tissue will lead to a form of the Burr probability distribution functions for speckle amplitudes. This hypothesis is generalized and tested in theory, simulations, and experiments. Approach We argue that two broadly applicable conjectures are sufficient to justify the applicability of the Burr distribution for speckle from a number of acoustical, optical, and other puls