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Effectiveness of the Kozachenko-Leonenko estimator for generalized entropic forms.

In this Brief Report we discuss the effectiveness of the Kozachenko-Leonenko entropy estimator when generalized to cope with entropic forms customarily applied to study systems evincing asymptotic scale invariance and dependence (either of linear or nonlinear kind). We show that when the variables are independently and identically distributed the estimator is only valuable along the whole domain if the data follow the uniform distribution, whereas for other distributions the estimator is only effectual in the limit of the Boltzmann-Gibbs-Shanon entropic form. We also analyze the influence of the dependence (linear and nonlinear) between variables on the accuracy of the estimator between variables. As expected in the last case the estimator loses efficiency for the Boltzmann-Gibbs-Shanon entropic form as well.