Extensions and closures of exponential families

The variation distance closures of exponential families and their log-convex subfamilies will be presented. They provide nontrivial natural boundaries to general exponential families viewed as manifolds. Closures in a reversed information divergence, rI-closure, and its statistical relevance will be discussed. An exponential family is constructed such that its rI-closure, is neither rI-closed nor log-convex.