| Abstract: | The problem of fitting a probability distribution, here log-Pearson Type III distribution, to extreme floods is considered from the point of view of two numerical and three non-numerical criteria. The six techniques of fitting considered include classical techniques (maximum likelihood, moments of logarithms of flows) and new methods such as mixed moments and the generalized method of moments developed by two of the co-authors. The latter method consists of fitting the distribution using moments of different order, in particular the SAM method (Sundry Averages Method) uses the moments of order 0 (geometric mean), 1 (arithmetic mean), –1 (harmonic mean) and leads to a smaller variance of the parameters. The criteria used to select the method of parameter estimation are:| | - the two statistical criteria of mean square error and bias; | | | - the two computational criteria of program availability and ease of use; | | | - the user-related criterion of acceptability. |
These criteria are transformed into value functions or fuzzy set membership functions and then three Multiple Criteria Decision Modelling (MCDM) techniques, namely, composite programming, ELECTRE, and MCQA, are applied to rank the estimation techniques. |
