We propose a simple method of construction of new families of φ-divergences. This method called convex standardization is applicable to convex and concave functions ψ(t) twice continuously differentiable in a neighborhood of t = 1 with nonzero second derivative at the point t = 1. Using this method we introduce several extensions of the LeCam, power, χ and Matusita divergences. The extended fam...

We propose to interpret distribution model risk as sensitivity of expected loss to changes in the risk factor distribution, and to measure the distribution model risk of a portfolio by the maximum expected loss over a set of plausible distributions defined in terms of some divergence from an estimated distribution. The divergence may be relative entropy, a Bregman distance, or an f -divergence....

recently, we have used the symmetric bracket of vector fields, and developed the notion of the symmetric derivation. using this machinery, we have defined the concept of symmetric curvature. this concept is natural and is related to the notions divergence and laplacian of vector fields. this concept is also related to the derivations on the algebra of symmetric forms which has been discus...

We give bounds on the difference between weighted arithmetic mean and geometric mean. These imply refined Young inequalities reverses of inequality. also study some properties Applying newly obtained inequalities, we show results Tsallis divergence, R\'{e}nyi Jeffreys-Tsallis divergence Jensen-Shannon-Tsallis divergence.

In this paper, we investigate some inferential properties of the upper record Lomax distribution. Also, we will estimate the upper record of the Lomax distribution parameters using methods, Moment (MME), Maximum Likelihood (MLE), Kullback-Leibler Divergence of the Survival function (DLS) and Baysian. Finally, we will compare these methods using the Monte Carlo simulation.

Jensen-Shannon, J-divergence and Arithmetic-Geometric mean divergences are three classical divergence measures known in the information theory and statistics literature. These three divergence measures bear interesting inequality among the three non-logarithmic measures known as triangular discrimination, Hellingar’s divergence and symmetric chi-square divergence. However, in 2003, Eve studied ...

Tools like SourceForge or BSCW have popularized virtual teams through the web. They allow people to work together distributed across space, time and organization. A member of a virtual team can work disconnected on his private copies of shared objects with cycles of divergence-convergence. Divergence occurs when people are working “insulated” in their private workspaces and convergence takes pl...

In this paper, penalized power-divergence test statistics have been defined and their exact size properties to test a nested sequence of log-linear models have been compared with ordinary power-divergence test statistics for various penalization, λ and main effect values. Since the ordinary and penalized powerdivergence test statistics have the same asymptotic distribution, comparisons have bee...

A divergence function defines a Riemannian metric g and dually coupled affine connections ∇ and ∇∗ with respect to it in a manifold M . When M is dually flat, that is flat with respect to ∇ and ∇∗, a canonical divergence is known, which is uniquely determined from (M, g,∇,∇∗). We propose a natural definition of a canonical divergence for a general, not necessarily flat, M by using the geodesic ...

In this paper, we analyze variation in spectral reflectance and color pattern among populations to demonstrate dramatic divergence between four distinct morphs of the mimic poison frog Ranitomeya imitator. We also analyze genetic divergence in d-loop mtDNA sequences between populations. We then use coalescent-based simulations to demonstrate that the high levels of observed phenotypic divergenc...