具有Softmax函数应用的剩余和过去离散Tsallis与Renyi熵。

Residual and Past Discrete Tsallis and Renyi Extropy with an Application to Softmax Function.

作者信息

Jawa Taghreed M, Fatima Nahid, Sayed-Ahmed Neveen, Aldallal Ramy, Mohamed Mohamed Said

机构信息

Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.

Department of Mathematics & Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.

出版信息

Entropy (Basel). 2022 Nov 27;24(12):1732. doi: 10.3390/e24121732.

DOI:10.3390/e24121732

PMID:36554137

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9777819/

Abstract

In this paper, based on the discrete lifetime distribution, the residual and past of the Tsallis and Renyi extropy are introduced as new measures of information. Moreover, some of their properties and their relation to other measures are discussed. Furthermore, an example of a uniform distribution of the obtained models is given. Moreover, the softmax function can be used as a discrete probability distribution function with a unity sum. Thus, applying those measures to the softmax function for simulated and real data is demonstrated. Besides, for real data, the softmax data are fit to a convenient ARIMA model.

摘要

在本文中，基于离散寿命分布，引入了Tsallis熵和Renyi熵的剩余部分及过去部分作为新的信息度量。此外，还讨论了它们的一些性质以及它们与其他度量的关系。此外，给出了所得模型均匀分布的一个例子。而且，softmax函数可以用作总和为1的离散概率分布函数。因此，展示了将这些度量应用于softmax函数以处理模拟数据和真实数据的情况。此外，对于真实数据，将softmax数据拟合到一个合适的自回归积分移动平均（ARIMA）模型。