ABSTRACT
The method of moments has the merit of being very simple to define and usually simple to implement; often, the equations to be solved are algebraic equations leading to explicit solutions. The concept of the maximum likelihood estimate has been traced back to Daniel Bernoulli and Johann Heinrich Lambert in the eighteenth century. Scholz has proposed an alternative and more general definition of the maximum likelihood estimation (MLE), capable of handling the non-invertible transformation case without introducing additional concepts such as induced likelihood. Once the MLE has been found, an evaluation of its 'quality' is required, to be able to form some idea about the plausible deviation between the estimate and the true parameter. Numerical methods are employed in a number of ways, either for direct maximization of the log-likelihood or for solving the likelihood equations.
