Nonparametric estimation of past extropy under $$\alpha $$-mixing dependence condition

Abstract

Di Crescenzo and Longobardi (J Appl Prob 39, 434–440, 2002), introduced the concept of past entropy for measuring uncertainty contained in past lifetime of random variables. By analogous to past entropy, Krishnan et al. (J Korean Stat Soc, 49, 457–474, 2020) defined the concept of past extropy. In this work, we propose nonparametric estimator for the past extropy, where the observations under consideration exhibit $$\alpha $$ -mixing dependence. Asymptotic properties of the proposed estimator are derived under suitable regularity conditions. A Monte–Carlo simulation study is carried out to compare the performance of the estimators using the mean squared error.