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

This paper demonstrates that 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. It also presents a function that gives the entropy of these related variates, using only statistics of the logarithm of the variate plus a constant, regardless of the nature or the parameters of the variates involved.