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Determination of the amplitude distribution and density of shot processes is a problem of longstanding interest. In this paper we present approximations for these distributions and densities whose salient features are accuracy and ease of computation. The parameters that characterize the approximations are determined by the lowerorder moments or cumulants of the shot process. To illustrate the accuracy of the approximations, they are compared with the exact functions in three cases. A logarithmic error measure is introduced and a simple approximation for it is given.