论文标题
关于累积的tsallis熵
On cumulative Tsallis entropies
论文作者
论文摘要
我们研究了累积的Tsallis熵，这是一种信息度量，最近作为经典Tsallis差异熵的累积版本引入了，这本身就是Boltzmann-Gibbs统计的概括。此功能在这里被视为通过某种功率重量函数的预期平均残留寿命的扰动。这种观点导致引入双重累积的tsallis熵以及两个连贯的风险家族衡量概括基于平均残留寿命的家族。我们以$ {\ Mathcal l} _p $ - 空格的形式来表征累积tsallis熵的有限性，并显示它们如何确定基础分布。该功能的范围在各种约束下精确描述，最佳界限改善了文献中先前可用的所有范围。 tsallis差分熵的最大化导致经典的$ q- $高斯分布，这是高斯具有有限范围或重尾巴的概括，但累积的tsallis熵的最大化导致对逻辑分布的类似扰动。
We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of ${\mathcal L}_p$-spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical $q-$Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution.
