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Entropy Differential Metric, Distance and Divergence Measures in Probability Spaces - A Unified Approach

机译：概率空间中的熵微分度量，距离和发散度量 - 一种统一的方法

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摘要

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 thi-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 inter-relationships. (Author)

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作者
Burbea, J.; Rao, C. R.;
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年度 1980
页码 p.1-38
总页数 38
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Probability distribution functions; Entropy; Estimates; Measure theory; Geodesics; Statistical samples; Heuristic methods; Matrices(Mathematics); Theorems; Normal distribution;

机译：概率分布函数;熵;估计;测量理论;测地学;统计样本;启发式方法;矩阵（数学）;定理;正态分布;

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2. An Implicit Relation Approach in Metric Spaces under -Distance and Application to Fractional Differential Equation [J] . Reena Jain, Hemant Kumar Nashine, Santosh Kumar Journal of Function Spaces . 2021,第a期

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3. On the probability that finite spaces with random distances are metric spaces [J] . Vania Mascioni Discrete mathematics . 2005,第1a3期

机译：关于具有随机距离的有限空间是度量空间的概率
4. Measure divergence degree of basic probability assignment based on Deng relative entropy [C] . Liguo Fei, Yong Deng Chinese Control and Decision Conference . 2016

机译：基于邓相对熵的基本概率分配的分解程度
5. Reproducing Kernel Space Embeddings and Metrics on Probability Measures. [D] . Sriperumbudur Vangeepuram, Bharath Kumar. 2010

机译：复制概率度量的内核空间嵌入和度量。
6. THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES [O] . STEVEN N. EVANS, ILYA MOLCHANOV -1

机译：度量度量空间的半数及其无限可分的概率度量
7. Entropy differential metric, distance and divergence measures in probability spaces: A unified approach [O] . Burbea Jacob, Rao C.Radhakrishna 1982

机译：概率空间中的熵微分度量，距离和散度度量：统一方法

Entropy Differential Metric, Distance and Divergence Measures in Probability Spaces - A Unified Approach

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