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On the estimation of extropy. (English) Zbl 1417.62015

Given \(n\) i.i.d. samples \(X_1, \dots, X_n\) from a distribution \(P_f\) with density \(f\), the authors investigate different methods to estimate the extropy \[ J\left(P_f\right) = -\frac12 \int f^2 \left(x\right) \,\mathrm d x. \] They first recall previously studied estimators, and then derive four new methods to estimate \(J\left(P_f\right)\) and prove their consistency. All aforementioned estimators are compared in a simulation study and their performance on real world data is investigated.

MSC:

62B10 Statistical aspects of information-theoretic topics
62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
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