In this paper, we propose nonparametric estimators for varextropy function of an absolutely continuous random variable. Consistency of the estimators is established under suitable regularity conditions. Moreover, a simulation study is performed to compare the performance of the proposed estimators based on mean squared error (MSE) and bias. Furthermore, by using the proposed estimators some tests are constructed for uniformity. It is shown that the varextropybased test proposed here performs well compared to the power of the other uniformity hypothesis tests.

翻译：本文针对绝对连续随机变量的变熵函数提出了非参数估计量。在适当的正则性条件下，我们证明了这些估计量的一致性。此外，通过模拟研究，基于均方误差（MSE）和偏差比较了所提出估计量的性能。进一步地，利用所提出的估计量构建了若干均匀性检验。结果表明，本文提出的基于变熵的检验方法在检验功效上优于其他均匀性假设检验。