  In this paper, we propose a new class of distributions by exponentiating the
random variables associated with the probability density functions of composite
distributions. We also derive some mathematical properties of this new class of
distributions including the moments and the limited moments. Specifically, two
special models in this family are discussed. Two real data sets were chosen to
assess the performance of these two special exponentiated composite models.
When fitting to these two data sets, theses two special exponentiated composite
distributions demonstrate significantly better performance compared to the
original composite distributions.
