Abstract
In this paper, we investigate the mixture arc on generalized statistical manifolds. We ensure that the generalization of the mixture arc is well defined and we are able to provide a generalization of the open exponential arc and its properties. We consider the model of a -family of distributions to describe our general statistical model.
Highlights
In the geometry of statistical models, information geometry [1,2,3] is the part of probability theory dedicated to investigate probability density functions equipped with differential geometry structure
The statistical manifold Pμ can be equipped with a structure of C ∞ -Banach
Each connected component of the statistical manifold gives φ rise to a φ-family of probability distributions Fc
Summary
In the geometry of statistical models, information geometry [1,2,3] is the part of probability theory dedicated to investigate probability density functions equipped with differential geometry structure. A differential-geometric structure to the multi-parameter families of distributions was provided in [4]. Divergence function is an essential topic in information geometry, for both, parametric and non-parametric cases, since a metric and dual connections can be induced from a divergence [7,8,9,10]. To find an information-geometrical foundation for multi-parameter families of probability distributions, with a more general description, is one of topics of interest in information geometry [11,12,13,14]
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