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Echoes from patches of fish fluctuate significantly from ping to ping as the sonar beam is swept across the patches. The fluctuations can be strongly non-Rayleigh because 1) there can be a small number of targets in the beam at a time, 2) the distribution of fish can be inhomogeneous, or "patchy", and 3) the echoes are weighted by the non-uniform response of the sonar beam. We have previously identified two distributions to describe the statistical behavior of non-Rayleigh echoes from fish - the K-distribution for patches of multiple unresolved fish and a power law distribution for individual resolved fish. The Redistribution has been shown in previous studies (Abraham and Lyons, IEEE J. Ocean. Eng. 27: 800-813, 2002) to describe the statistics of targets with a Gamma distribution of echo amplitude. The power law distribution is based on the method proposed by Ehrenberg et al. for circular aperture transceivers (J. Acoust. Soc. Am. 69: 955-962, 1981). In this paper, we provide a more general physical interpretation to the R-distribution and develop a generalized power-law distribution to include beampattern effect. In addition, we compare the data collected in the 2-10 kHz range with Atlantic herring with the model predictions for two types of groupings of echoes - within patches and across patches. The Rullback-Leibler (RL) distances between the observed and theoretically predicted distributions showed that for echoes within patches, Rayleigh distribution can reasonably describe the fish echoes amplitude while for echoes across patches, the echo amplitude can be characterized by either the R-distribution or a mixed distribution that involves the power law distribution of sonar beam, depending on whether the echoes can be resolved.