Anewfour-parameter model called the gamma–exponentiated exponential-Weibull distribution is being introduced in this paper. The new model turns out to be quite flexible for analyzing positive data. Representations of certain statistical functions associated with this distribution are obtained. Some special cases are pointed out as well. The parameters of the proposed distribution are estimated by making use of the maximum likelihood approach. This density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions as measured by the Anderson--Darling and Cramér--von Mises goodness–of–fit statistics. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as the physical and biological sciences, hydrology, medicine, meteorology and engineering.