Deformed logarithms and entropies
Deformed logarithms and entropies
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变形对数和熵
DOI：
10.1016/j.physa.2004.03.075
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发表时间：
2004
影响因子：
3.3
通讯作者：
A. M. Scarfone
中科院分区：
文献类型：
--
作者：
Giorgio Kaniadakis;M. Lissia;A. M. Scarfone
通过求解MaxEnt原理引入的微分函数方程，我们得到一类二参数变形对数并构造相应的二参数广义迹形式熵。广义分布源自这些广义熵，其方式与高斯分布源自香农熵相同，香农熵是该族的特殊极限情况。我们确定了变形对数保留对数最重要属性的参数区域，并表明重要的现有熵概括作为特殊情况包含在这个二参数类中。
By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.