In many statistical studies, the measure of uncertainties like entropy, extropy, varentropy and varextropy of a distribution function is of prime interest. This paper proposes estimators of extropy and varextropy. Proposed estimators are consistent. Based on extropy estimator, a test of symmetry is given. The proposed test has the advantage that we do not need to estimate the centre of symmetry. The critical value and power of the proposed test statistics have been obtained. The test procedure has been implemented on six real-life data sets to verify its performance in identifying the symmetric nature.

翻译：在许多统计研究中，分布函数的不确定性度量（如熵、外熵、方差熵和方差外熵）具有重要研究意义。本文提出了外熵和方差外熵的估计量，所提出的估计量具有一致性。基于外熵估计量，本文给出了一种对称性检验方法。该检验方法的优势在于无需估计对称中心。我们得到了所提检验统计量的临界值和检验功效，并在六个真实数据集上实施了该检验程序，以验证其识别对称性的性能。