There are different parameter estimation Techniques like MLE, Methods of moments, etc. but how do we know which method is more appropriate to estimate a parameter in a given model?
The density function parameters of the Pearson distribution III are determined by known formulas as a functions of the distribution moments. Moments estimates are computed from the sample data and are substituted into formulas. This is the most practical way of estimating.
As far as I know, the method of moments has the advantage of simplicity, however, it is not often available. On the other hand, MLE is based on a mathematical expression, hence it is applicable to most estimation scenarios.