On the <i>q</i> -Gamma distribution: Properties and inference

Abstract In this paper, we introduce a new q -Gamma probability distribution which is an extension of the classical Gamma distribution in the context of q -calculus. It is also a generalization of the q -exponential distribution. The main properties of the proposed model are presented. Its non-centered moments of any order were explicitly computed. In particular, the kurtosis and skewness were explicitly determined. Moreover, the maximum-likelihood estimation method of the parameters was developped. The performance of the estimation approach as well as the Metropolis-Hastings-based generation method were studied through several numerical experiments. In addition, a characterization of the q -exponential distribution is established using the truncated moments.