کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1147166 957555 2009 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On the geometry of generalized Gaussian distributions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز عددی
پیش نمایش صفحه اول مقاله
On the geometry of generalized Gaussian distributions
چکیده انگلیسی

In this paper we consider the space of those probability distributions which maximize the qq-Rényi entropy. These distributions have the same parameter space for every qq, and in the q=1q=1 case these are the normal distributions. Some methods to endow this parameter space with a Riemannian metric is presented: the second derivative of the qq-Rényi entropy, the Tsallis entropy, and the relative entropy give rise to a Riemannian metric, the Fisher information matrix is a natural Riemannian metric, and there are some geometrically motivated metrics which were studied by Siegel, Calvo and Oller, Lovrić, Min-Oo and Ruh. These metrics are different; therefore, our differential geometrical calculations are based on a new metric with parameters, which covers all the above-mentioned metrics for special values of the parameters, among others. We also compute the geometrical properties of this metric, the equation of the geodesic line with some special solutions, the Riemann and Ricci curvature tensors, and the scalar curvature. Using the correspondence between the volume of the geodesic ball and the scalar curvature we show how the parameter qq modulates the statistical distinguishability of close points. We show that some frequently used metrics in quantum information geometry can be easily recovered from classical metrics.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Multivariate Analysis - Volume 100, Issue 4, April 2009, Pages 777–793
نویسندگان
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