The Zenga (1984) inequality curve λ(p) is constant in p for Type I Pareto distributions. We show that this property holds exactly only for the Pareto distribu- tion and, asymptotically, for distributions with power tail with index α, with α > 1. Exploiting these properties one can develop powerful tools to analyze and estimate the tail of a distribution. An estimator for α is discussed. Inference is based on an estimator of λ ( p) which utilizes all sample information for all values of p. The prop- erties of the proposed estimation strategy is analyzed theoretically and by means of simulations.