Gamma-Laguerre Formalism: Rigorous Approach and Application to Hydrologic Time Series

Previous work by various authors has shown that gamma-Laguerre distributions are appropriate for hydrologic applications because they offer the flexibility necessary to fit both the bulk and tails of empirical distributions, as well as a handy estimation formalism. The present work solves problems that still remain in gamma-Laguerre parameter estimation formalism: evaluating the highest degree of Laguerre polynomial and avoiding decreasing intervals in fitted probability distribution functions. From a pool of over 200 maximal rainfall and maximal discharge time series from all over the world that have been analyzed, a couple of examples, located in Mexico City and Niamey, respectively, are presented to illustrate the functionality of the formalism.