Comparison of the alternative parameter estimators of Pearson distributions by robustness criteria

Pearson's differential equation is used for fitting a distribution to data set. The has some alternative moment-based estimators (depending on the transformation data). estimator when no made set 4 elements, and that require any have 3 elements. We describe all elements of by corresponding vectors. One factors affecting preference an robustness. use covariance matrix, bias, relative efficiency influence function as our robustness criteria. Our aim compare performance specific distributions (namely Type I, IV, VI III). 10,000 samples with sizes were selected replacement. Also, we evaluated over real-life data. Considering results, there best in Depending criterion be based, preferred varies.