Received: 19 January 2018 / Revised: 18 February 2018 / Accepted: 21 February 2018 / Published: 25 February 2018

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**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

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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 $\phi $ -family of distributions to describe our general statistical model.
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(This article belongs to the Special Issue Statistical Distances and Geometry—Selected Papers from GSI conference 2017)