The Gumbel Mixed Model Applied to Analysis for Frequency Maximum Precipitations in North Karun Basin

A bivariate extreme value distribution, namely the Gumbel mixed model constructed from Gumbel marginal distributions is employed to analyze the joint distribution of correlated storm peak (maximum rainfall intensity) and amount. Based on its marginal distributions, the joint distribution, the conditional probability distribution, and the associated return periods can be deduced. Parameters of the bivariate distribution model are estimated based on its marginal distributions by the method of moments (MM). The usefulness of the model is demonstrated by using it to represent multivariate probable maximum precipitation events at the north Karun basin meteorological stations (Armand, Barez, Marghak and Pol-e-Shalo) in Iran.