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Recursive and non-recursive kernel estimation of negative cumulative residual extropy under $$\alpha $$ α -mixing dependence condition
Ricerche di Matematica ( IF 1.2 ) Pub Date : 2021-06-18 , DOI: 10.1007/s11587-021-00605-0
R. Maya , M. R. Irshad , K. Archana

The Shannon’s entropy function has a complementary dual function namely extropy and it facilitates the comparison of uncertainties of two random variables (see Lad et al. Stat Sci 30:40–58, 2015). Following the work of Lad et al. (Stat Sci 30:40–58, 2015), various generalizations/extensions of extropy measure are discussed in the literature analogous to that of Shannon’s entropy. Accordingly, a negative cumulative residual extropy is introduced by Tahmasebi and Toomaj (Commun Stat Theor Methods, 2020. https://doi.org/10.1080/03610926.2020.1831541). In the present work, we provide nonparametric kernel type estimators for the negative cumulative residual extropy based on the observations under study are dependent. Various properties including asymptotic properties of the proposed estimators are derived under suitable regularity conditions. A Monte-Carlo simulation study is carried out to find out the bias and mean squared error of the estimators.



中文翻译:

$$\alpha $$ α-混合依赖条件下负累积残差熵的递归和非递归核估计

香农的熵函数具有互补的对偶函数,即熵,它有助于比较两个随机变量的不确定性(参见 Lad 等人。Stat Sci 30:40–58, 2015)。继 Lad 等人的工作之后。(Stat Sci 30:40–58, 2015),在与香农熵类似的文献中讨论了熵测度的各种概括/扩展。因此,Tahmasebi 和 Toomaj (Commun Stat Theor Methods, 2020. https://doi.org/10.1080/03610926.2020.1831541) 引入了负累积残差熵。在目前的工作中,我们根据研究中的观察结果为负累积残差熵提供非参数核类型估计器。在合适的规律性条件下导出了包括所提出的估计量的渐近特性在内的各种特性。

更新日期:2021-06-18
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