Based on Monte Carlo method,four different weighted function moment methods for Pearson Ⅲ distribution which were developed in China are first compared by using the evaluation standard considering unbiasness and effectiveness of parameters and design values.

Based upon the Monte-Carlo experimentsthe results of the unbiasness and efficiency of the parameters and design flood valuesshow that above formulae are effective, so the applied scope of weighted function momentS method is e.

In the long life and high reliability design and analysis of structures, the unbiasedness of statistical property of sample is more important.

In this paper,samples as a sensitive issue in two kinds of random survey answered model,from two angles of a large sample theory and a small sample theory respectively,the estimates obtained by the quantity of unbiasedness,effectiveness,consistency of the strength of the areas of evaluation and assessment are to survey it is reasonable and effective.

In the light of unbiasedness and validity of model, we identify the rigidity rotation model and rotation with strain model.

Through the statistically comparative analysis of these methods,it comes to a conclusion that the unbias and robustness of liner moments are better than the others .

The properties of four factorized chi-square forms, which are used in minimization of correlated data, are studied, including their biasness and unbiasedness.