Generalized Arithmetic and Geometric Mean Divergence Measure and their Statistical Aspects

On Unified Generalizations of Relative Jensen--Shannon and Arithmetic--Geometric Divergence Measures, and Their Properties

In this paper we shall consider one parametric generalization of some non-symmetric divergence measures. The \textit{non-symmetric divergence measures} are such as: Kullback-Leibler \textit{relative information}, $χ^2-$\textit{divergence}, \textit{relative J -- divergence}, \textit{relative Jensen -- Shannon divergence} and \textit{relative Arithmetic -- Geometric divergence}. All the generalizations considered can be written as particular cases of Csiszár's \textit{f-divergence}. By putting some conditions on the probability distribution, the aim here is to develop bounds on these measures an…

On Mean Divergence Measures

Arithmetic, geometric and harmonic means are the three classical means famous in the literature. Another mean such as square-root mean is also known. In this paper, we have constructed divergence measures based on nonnegative differences among these means, and established an interesting inequality by use of properties of Csiszar's f-divergence. Connections of new mean divergences measures with classical divergence measures such as Jeffreys-Kullback-Leibler J-divergence, Sibson-Burbea-Rao Jensen difference divergence measure and Taneja's arithmetic - geometric mean divergence are also establish…

Generalized Non-Symmetric Divergence Measures and Inequalities

In this paper we consider one parameter generalizations of some non - symmetric divergence measures. Measures are \textit{relative information}, $χ^2 - $\textit{divergence}, \textit{relative J-divergence}, \textit{relative Jensen-Shannon divergence}and \textit{relative arithmetic and geometric divergence}. All the generalizations considered can be written as particular cases of Csiszár \textit{f-divergence}. By conditioning the probability distributions, relationships among the \textit{relative divergence measures}are obtained.

退火路径的变分表示：单调嵌入下的Bregman信息

Variational Representations of Annealing Paths: Bregman Information under Monotonic Embedding

本文通过单调嵌入下的Bregman散度框架，证明拟算术均值在变换后最小化期望散度，从而揭示退火路径中间密度的变分表示及其与常见散度泛函的关联。

On a Difference of Jensen Inequality and its Applications to Mean Divergence Measures

In this paper we have considered a difference of Jensen's inequality for convex functions and proved some of its properties. In particular, we have obtained results for Csiszár \cite{csi1} $f-$divergence. A result is established that allow us to compare two measures under certain conditions. By the application of this result we have obtained a new inequality for the well known means such as arithmetic, geometric and harmonic. Some divergence measures based on these means are also defined.

Bregman divergences based on optimal design criteria and simplicial measures of dispersion

In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is embedded in the wider theory of divergences and distances between distributions which includes Kullback-Leibler, Jensen-Shannon, Jeffreys-Bregman divergence and Bhattacharyya distance. A general construction is given based on defining a directional derivative of a function $ϕ$ from one distribution to the other whose concavity or strict concavity influences the…