Collision Entropy Estimation in a One-Line Formula

Integer-order Rényi entropies are synthetic indices useful for the characterization of probability distributions. In recent decades, numerous studies have been conducted to arrive at valid estimates of these indices starting from experimental data, to derive a suitable classification method for the underlying processes. However, optimal solutions have not been reached yet. A one-line formula limited to the estimation of collision entropy is presented here. The results of some specific Monte Carlo experiments gave evidence of its validity even for the very low densities of the data spread in the sample space. The strengths of this method are unbiased consistency, generality and minimum computational cost.