Α-divergence Derived as the Generalized Rate Function in a Power-law System
نویسندگان
چکیده
The generalized binomial distribution in Tsallis statistics (power-law system) is explicitly formulated from the precise q-Stirling’s formula. The α-divergence (or q-divergence) is uniquely derived from the generalized binomial distribution in the sense that when α → −1 (i.e., q → 1) it recovers KL divergence obtained from the standard binomial distribution. Based on these combinatorial considerations, it is shown that α-divergence (or q-divergence) is appeared as the generalized rate function in the large deviation estimate in Tsallis statistics.
منابع مشابه
Generalized Differential Quadrature Method for Vibration Analysis of Cantilever Trapezoidal FG Thick Plate
This paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equa...
متن کاملFrequency Analysis of FG Sandwich Rectangular Plates with a Four-Parameter Power-Law Distribution
An accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The two-constituent FGS plate consists of ceramic and metal graded thr...
متن کاملGeneralized Estimating Equation for the Student-t Distributions
In [12], it was shown that a generalized maximum likelihood estimation problem on a (canonical) α-power-law model (M-family) can be solved by solving a system of linear equations. This was due to an orthogonality relationship between the M-family and a linear family with respect to the relative α-entropy (or the Iα-divergence). Relative α-entropy is a generalization of the usual relative entrop...
متن کاملPower Function Distribution Characterized by Dual Generalized Order Statistics
The dual generalized order statistics is a unified model which contains the well known decreasingly ordered random data such as (reversed ordered) order statistics and lower record values. In the present paper, some characterization results on the power function distribution based on the properties of dual generalized order statistics are provided. The results are proved without any rest...
متن کاملAn Investigation of Stress and Deformation Behavior of Functionally Graded Timoshenko Beams subjected to Thermo-Mechanical Load
A functionally graded material beam with generalized boundary conditions is contemplated in the present study in order to examine the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been deliberate in including a wide range of materials and material properties. The variation of material properties has be...
متن کامل