Method of moments of the Halphen distribution parameters

Halphen laws have been proposed as a complete system of distributions with sufficient statistics that lead to estimation with minimum variance. The Halphen system provides a flexibility to fit a large variety of data sets from natural events. In this paper we present the method of moments (MM) to estimate the Halphen type B and IB distribution parameters. Their computation is very fast when compared to those given by the maximum likelihood method (ML). Furthermore, this estimation method is very easy to implement since the formulae are explicit. Some simulations show the equivalence of both methods when estimating the quantiles for finite sample size.