The Ristic-Balakrishnan-G Family of Distributions: Mathematical Properties and Applications

In this article, with the help of exponentiated-G distribution, we obtain extensions for the Probability density function and Cumulative distribution function, moments and moment generating functions, mean deviation, R$acute{e}$nyi and Shannon entropies and order Statistics of this family of distributions. We use maximum liklihood method of estimate the parameters and with the help of a real data set, we show the Risti$acute{c}$-Balakrishnan-$G$ family of distributions is a proper model for lifetime distribution.