Type II exponentiated class of distributions: The gamma model case

Recently, there is a great interest by researchers in the topic of deriving new probability distributions. This paper is in this direction. Here we are going to introduce a new class of distributions that we called type II exponentiated. This class is based on the same bases on which the class of Gupta et al. which was presented in 1998, which was named exponentiated. Here, we will named the class of Gupta et al. as type II exponentiated to discriminate it of our class which will introduced here. Instead of doing the analogy on the basis of the distribution function formula of the greatest order statistic as in Gupta et al. class, we have done here the analogy on the basis of the distribution function formula of the smallest order statistic. The type II Exponentiated Gamma distribution (type II EGD) and its properties is presented here to clarify our point of view. Some properties of the type I Gamma distribution which the researchers did not address will be treated also.