In this article we study some properties of a new family of distributions, namely Exponentiated Exponential distribution, discussed in Gupta, Gupta, and Gupta (1998). The Exponentiated Exponential family has two parameters (scale and shape) similar to a Weibull or a gamma family. It is observed that many properties of this new family are quite similar to those of a Weibull or a gamma family, th...