In this paper, an improved probabilistic method for flood analysis using the probable maximum flood, the beta function, and orthogonal Jacobi’s polynomials is proposed. The shape of the beta function depends on the sample's characteristics and the bounds of the phenomenon. On the other hand, a serial of Jacobi’s polynomials has been used improving the beta function and increasing its convergence degree toward the real flood probability density function. This mathematical model has been tested using a sample of 1000 generated beta random data. Finally, some practical applications with real data series, from important Quebec's rivers, have been performed; the model solutions for these rivers showed the accuracy of this new method in flood frequency estimation. Key words: probable maximum flood, beta function, orthogonal polynomials, distribution function, flood frequency estimation, data generation, convergency.
SHYREG, a national database of flood frequency estimation