The absolute minimum and maximum value problem and the Renyi entropy of order α

The Renyi entropy of order α can provide information on the minimum and maximum values of a probability distribution p=min{p₁ ,p₂,...,p_N} and p=max(p₁,p₂ ,...,p_N). The absolute minimum valve of a given probability distribution is shown to be related to the limit of the Renyi entropy, as α→-∞, or p=2^{-limα→-∞Hα(P)}. The absolute maximum valve is given by p=2^{-limα→∞Hα(P)}