The exponentiated gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called Transmuted exponentiated gamma (TEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the TEG distribution is provided. We derive the rth moment and moment generating function this distribution. Moreover, we discuss the maximum likelihood estimation of this distribution.
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Mohamed Hussian (2014) studied this question.