n explicit formula for fractional entropy
Delmestri A., Fioretto A., Sgarro A.
The fractional entropy HM(X) is an information measure derived from rate-distortion theory which measures the uncertainty contained in random experiment X when the pragmatic experimenter is not interested in the exact value of X, but is contented with a set of M possible outcomes where the actual outcome belongs (for M=1 one finds Shannon entropy). So far only an iterative algorithm (the general algorithm for rate-distortion functions) was available to compute HM(X) to the desired degree of accuracy. We give here an explicit (and perspicuous) formula for HM(X) which returns its exact value without computational trammels by expressing it as the difference of two usual Shannon entropies.