The Gumbel logistic model for representing a multivariate storm event

This study proposes the use of the Gumbel logistic model, the bivariate extreme value distribution with Gumbel marginals, to analyze the joint distribution of annual maximum storm peaks (maximum rainfall intensities) and the corresponding storm amounts which are mutually correlated. Parameters of the distribution are estimated using the method of moments (MM). On the basis of the marginal distributions of these random variables, the joint distribution, the conditional probability distribution, and the associated return periods can be readily deduced. The model is verified using observed daily rainfall data from the Tokushima meteorological station of Tokushima Prefecture, Japan. Results show that the model is suitable for representing the joint distribution of correlated storm peaks and amounts that are Gumbel distributed.