The use of the logarithm of the variate in the calculation of differential entropy among certain related statistical distributions

Abstract: This paper demonstrates that basic statistics (mean, variance) of the logarithm of the variate itself can be used in the calculation of differential entropy among random variables known to be multiples and powers of a common underlying variate. For the same set of distributions, the variance of the differential self-information is shown also to be a function of statistics of the logarithmic variate. Then entropy and its "variance" can be estimated using only statistics of the logarithmic variate plus constants, without reference to the traditional parameters of the variate.