Shahid Bahonar University of Kerman Journal of Mahani Mathematical Research 2251-7952 14 1 2025 01 01 Nonparametric estimators for varextropy under $\alpha$-mixing condition with appliction in exponential AR(1) model 45 61 4353 10.22103/jmmr.2024.22452.1529 EN Raheleh Zamini Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Faranak Goodarzi Department of Statistics, Faculty of Mathematical Sciences, University of Kashan, Kashan, Iran 0000-0002-3783-6632 Mohamad Salimi Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran Journal Article 2023 11 03 The goal of this paper is to study the problem of estimation of varextropy function under $\alpha$-mixing dependence condition. We propose nonparametric estimators for varextropy, residual varextropy and  past varextropy. Asymptotic properties of the proposed estimators  are investigated under regularity conditions. Moreover, the comparison of the proposed estimators for varextropy in terms of the bias and mean squared error has been done by Monte Carlo method. Furthermore, a real data example is presented. https://jmmrc.uk.ac.ir/article_4353_ac23aa767beac2476475b750a2a2df04.pdf