Large deviation estimates involving deformed exponential functions

Abstract

We study large deviation properties of probability distributions with either a compact support or a fat tail by comparing them with q-deformed exponential distributions. Our main result is a large deviation property for probability distributions with a fat tail.Comment: typos corrected, some addtional explanations, version to appear in Physica A, http://dx.doi.org/10.1016/j.physa.2015.05.09