ENTROPY DIFFERENTIAL METRIC, DISTANCE AND DIVERGENCE MEASURES IN PROBABILITY SPACES - A UNIFIED APPROACH
ENTROPY DIFFERENTIAL METRIC, DISTANCE AND DIVERGENCE MEASURES IN PROBABILITY SPACES - A UNIFIED APPROACH
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DOI：
10.1016/0047-259x(82)90065-3
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发表时间：
1982-01-01
影响因子：
1.6
通讯作者：
RAO, CR
中科院分区：
文献类型：
--
作者：
BURBEA, J;RAO, CR
本文致力于通过在概率分布的参数空间中引入二次微分度量来对概率空间进行度量化。为此，在概率空间上定义φ熵函数，并以其沿参数空间的切空间方向的Hessian矩阵作为度量。两个概率分布之间的距离计算为由度量引起的测地距离。本文还讨论了概率分布之间差异的三种度量及其相互关系。
The paper is devoted to metrization of probability spaces through the introduction of a quadratic differential metric in the parameter space of the probability distributions. For this purpose, a φ-entropy functional is defined on the probability space and its Hessian along a direction of the tangent space of the parameter space is taken as the metric. The distance between two probability distributions is computed as the geodesic distance induced by the metric. The paper also deals with three measures of divergence between probability distributions and their interrelationships.