A large literature deals with the problem of testing for a Pareto tail and estimating the parameters of the Pareto distribution. We first review the most widely used statistical tools and identify their weaknesses. Then we develop a methodology that exploits all the available information by taking into account the data generating process of the entire population. Accordingly, we estimate a lognormal-Pareto mixture via the EM algorithm and the maximization of the profile likelihood function. Simulation experiments and an empirical application to the size of the US metropolitan areas confirm that the proposed method works well and outperforms two commonly used techniques.
Keywords: Mixture distributions, EM algorithm, lognormal distribution, Pareto distribution.
