In this article, we study the so-called the Weibull Weibull distribution. General
explicit expressions for the quantile function, expansion of its density function, ordinary
and incomplete moments, moments of the residual and reversed residual lifes, order
statistics and Rényi and q–entropies are derived. The model parameters are estimated
using the maximum likelihood method. Simulation results are provided to assess the
accuracy and performance of the maximum likelihood estimators. The usefulness and
flexibility of the Weibull Weibull model are illustrated using real data sets.