A study of the Gamma-Pareto (IV) distribution and its applications

Pareto distributions and their close relatives and generalizations provide very flexible families of heavy-tailed distributions that may be used to model income distributions as well as a wide variety of other social and economic distributions. On the other hand, gamma distribution has a wide application in various social and economic spheres such as survival analysis, to model aggregate insurance claims, and the amount of rainfall accumulated in a reservoir etc. Combining the above two heavy-tailed distributions, using the technique by Alzaatreh etal. (2012), we define a new distribution, namely Gamma-Pareto (IV) distribution, hereafter called as GPD((IV)) distribution. Various properties of the GPD((IV)) are investigated such as limiting behavior, moments, mode, and Shannon entropy. Also some characterizations of the GPD((IV)) distribution are mentioned in this paper. Maximum likelihood method is proposed for estimating the model parameters. For illustrative purposes, real data sets are considered as applications of the GPD((IV)) distribution.