Q-log-distributions: Log-concavity and log-convexity

Abstract

Tsallis statistics along with Tsallis distributions have been attracting considerable attention of statisticians in recent years, since applications of the q-distributions can be found in various fields. However, only until recently, in 2018, a q -logarithm transformation has been considered in order to obtain new Tsallis distributions. In this paper, we introduce the q-log-distributions defined for $q > 1$ . We propose these models to be considered for modeling demographic data. We discuss the log-concavity and log-convexity of these models with emphasis on log-concavity. We extend the notions of log-concavity and log-convexity. We explore the shapes of the hazard rate functions and give bounds for the mean residual life function.