In this chapter we consider a deformation of the nonparametric exponential statistical models, using the Tsalli's deformed exponentials, to construct a Banach manifold modelled on spaces of essentially bounded random variables. As a result of the construction, this manifold recovers the exponential manifold given by Pistone and Sempi up to continuous embeddings on the modeling space. The (q)-divergence functional plays two important roles on the manifold; on one hand, the coordinate mappings are in terms of the class="InlineEquation" id="IEq7">(q)-divergence functional; on the other hand, this functional induces a Riemannian geometry for which the Amari's (alpha )-connections and the Levi-Civita connections appears as special cases of the (q)-connections induced, (igtriangledown ^{(q)}). The main result is the flatness (zero curvature) of the manifold.