On the method of moments approach applied to a (generalized) gamma population

In this article we propose for a generalized gamma population method of moment estimators for the three unknown parameters. This method of moment approach is based on estimating the unknown parameters of the log generalized gamma distribution. Contrary to the more classical method of moment approaches discussed in the literature the associated system of nonlinear equations satisfies the following properties. The system of nonlinear equations associated with these moment estimators do not have a solution if and only if the sample moment estimation of the skewness of a log generalized gamma distribution is outside a given interval. This might happen with a positive probability for small sample sizes and this probability goes to zero as the sample size increases. However, if the system of nonlinear equations has a solution the method of moment estimators are a unique solution of this system and this solution is easy to determine by applying a univariate bisection procedure. The efficiency of these methods of moment estimators are tested in the computational section against the classical maximum likelihood estimators. Based on these experiments we give some guidelines how to use these methods of moments estimators in practice.