Estimation in a Pareto Distribution: Theory & Computation

This paper treats the theoretical and computational problems of maximum likelihood parameter estimation in a Pareto distribution. Logarithmic likelihood estimating equations and the associated conditional log-likelihood function are derived, and expressions for the asymptotic variances and covariances of the parameters are given. Discussions pertinent to tests of hypotheses and the construction of simultaneous s-confidence contours are provided. The computations required for estimation are illustrated by an example in which the parameters are estimated by numerically maximizing the conditional log-likelihood function and by using an algorithm for global optimization which exploits the mathematical structure of this function. The parameter estimates obtained in this way are guaranteed to be those at which the likelihood function is globally maximum over the space of permissible parameter values. A Fortran program exists for performing these calculations.