Beta-Jacobi and Gamma-Laguerre functions as methods of analysis of hydrological extreme values; Case of the yearly maximum precipitation ; Las funciones Beta-Jacobi y Gamma-Laguerre como métodos de análisis de valores hidrológicos extremos. Caso de precipitaciones máximas anuales

The probability density functions Beta and Gamma improved by a series of orthogonal polynomials of type Jacobi and Laguerre respectively have been compared with the four most common functions used on the analysis of hydrological extreme values: Gumbel 1, 3 Parameter Log-Normal (LN3), General Extreme Values (GEV) and Log-Pearson III (LP3). These six functions have been used in order to fit an important number of samples However this paper only shows the results of one of them. The sample selected corresponds to the maximum precipitation over 24 hours data from the climatological Tacubaya station (Mexico, D.F.). All functions give, for the central quantiles estimatimates (from 10 to 50 years), equivalent values with differences below 3%. For estimates of quantiles with a year return period higher than 100 years, LN3 and GEV gives higher values than Beta-Jacobi and Gamma-Laguerre around 11%. The difference using Beta-Jacobi and Gamma-Laguerre is always below 3% of the estimated value even for the 1000 year return period. On the other hand, LP3 and Gumbel 1 give higher results compared with the four other functions for the year return periods higher than 50 years. The results obtained have shown that the higher order probability density functions due to their statistical properties, are a tool as valid as the functions internationally accepted nowadays, for the behavior analysis of hydrological extreme values. However; the functions here presented have qualities in their construction which facilitate to take into account more information, which is contained in the higher moments, improving the extreme values estimates and probably the realization of designs more economic and efficient. ; Las funciones de densidad de probabilidad Beta y Gamma, mejoradas por una serie de polinomios ortogonales de los tipos Jacobi y Laguerre respectivamente, han sido comparadas con cuatro funciones comúnmente utilizadas en el análisis de valores hidrológicos extremos: Gumbel tipo I, Log-Normal de 3 parámetros (LN3), General de Valores ...