Alizadeh Noughabi, Hadi; Jarrahiferiz, Jalil On the estimation of extropy. (English) Zbl 1417.62015 J. Nonparametric Stat. 31, No. 1, 88-99 (2019). 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. Reviewer: Frank Werner (Göttingen) Cited in 18 Documents MSC: 62B10 Statistical aspects of information-theoretic topics 62G07 Density estimation 62G20 Asymptotic properties of nonparametric inference Keywords:extropy; nonparametric kernel density estimation; local linear model; mean squared error; Monte Carlo simulation PDFBibTeX XMLCite \textit{H. Alizadeh Noughabi} and \textit{J. Jarrahiferiz}, J. Nonparametric Stat. 31, No. 1, 88--99 (2019; Zbl 1417.62015) Full Text: DOI References: [1] Chhikara, R. S.; Folks, J. L., The Inverse Gaussian Distribution as a Lifetime model, Technometrics, 19, 461-468 (1977) · Zbl 0372.62076 · doi:10.1080/00401706.1977.10489586 [2] Correa, J. C., A new Estimator of entropy, Communications in Statistics-Theory and Methods, 24, 2439-2449 (1995) · Zbl 0875.62030 · doi:10.1080/03610929508831626 [3] Grzegorzewski, P.; Wieczorkowski, R., Entropy-based Goodness-of-fit Test for Exponentiality, Communications in Statistics-Theory and Methods, 28, 1183-1202 (1999) · Zbl 0919.62041 · doi:10.1080/03610929908832351 [4] Lad, F.; Sanfilippo, G.; Agro, G., Extropy: Complementary Dual of Entropy, Statistical Science, 30, 40-58 (2015) · Zbl 1332.62027 · doi:10.1214/14-STS430 [5] Lee, S.; Vonta, I.; Karagrigoriou, A., A Maximum Entropy Type Test of fit, Computational Statistics & Data Analysis, 55, 2635-2643 (2011) · Zbl 1464.62117 · doi:10.1016/j.csda.2011.03.012 [6] Mudholkar, G. S.; Natarajan, R.; Chaubey, Y. P., A Goodness-of-fit Test for the Inverse Gaussian Distribution Using its Independence characterization, Sankhya B, 63, 362-374 (2001) · Zbl 1192.62131 [7] Noughabi, H.; Noughabi, R., On the Entropy estimators, Journal of Statistical Computation and Simulation, 83, 784-792 (2013) · Zbl 1431.62025 · doi:10.1080/00949655.2011.637039 [8] Qiu, G., The Extropy of Order Statistics and Record values, Statistics & Probability Letters, 120, 52-60 (2017) · Zbl 1349.62165 · doi:10.1016/j.spl.2016.09.016 [9] Qiu, G.; Jia, K., Extropy Estimators with Applications in Testing uniformity, Journal of Nonparametric Statistics, 30, 182-196 (2018) · Zbl 1388.62133 · doi:10.1080/10485252.2017.1404063 [10] Qiu, G.; Jia, K., The Residual Extropy of Order statistics, Statistics & Probability Letters, 133, 15-22 (2018) · Zbl 1440.62164 · doi:10.1016/j.spl.2017.09.014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.