Moment-based inference for Pearson's quadratic q subfamily of   distributions
  The author uses a Stein-type covariance identity to obtain moment estimators for the parameters of the quadratic polynomial subfamily of Pearson distributions. The asymptotic distribution of the estimators is obtained, and normality and symmetry tests based on it are provided. Simulation is used to compare the performance of the proposed tests with that of other existing tests for symmetry and normality. 
Giorgos Afendras
math.ST stat.TH