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Varentropy of order statistics and some stochastic comparisons
Communications in Statistics - Theory and Methods ( IF 0.8 ) Pub Date : 2021-01-03 , DOI: 10.1080/03610926.2020.1861299
S. Maadani 1 , G. R. Mohtashami Borzadaran 1 , A. H. Rezaei Roknabadi 1
Affiliation  

Abstract

The variance of the log-likelihood function, which is called varentropy, is a measure of the concentration of information content around the Shannon entropy. This measure is widely applied in finite blocklength information theory and data compression. On the other hand, in the field of statistics, this measure has been used as an alternative of the kurtosis measure for continuous density functions that has a better performance. In this paper, we introduce a method for calculating this measure for the ith order statistic. We study the changes of the varentropy versus i for some distributions and show that in the symmetric distributions, under certain conditions, the median of the order statistics has minimum varentropy. Also, we introduce a new stochastic order based on the varentropy and relationships of it with the other stochastic orders.



中文翻译:

订单统计的变熵和一些随机比较

摘要

对数似然函数的方差(称为变熵)是香农熵周围信息内容集中度的量度。该度量广泛应用于有限块长度信息论和数据压缩。另一方面,在统计领域,该度量已被用作具有更好性能的连续密度函数的峰度度量的替代方案。在本文中,我们介绍了一种计算第i阶统计量的方法。我们研究了 varentropy 与i的变化对于某些分布,并表明在对称分布中,在某些条件下,阶统计的中位数具有最小的变熵。此外,我们基于变熵及其与其他随机顺序的关系引入了一种新的随机顺序。

更新日期:2021-01-03
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