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Abstract This article considers two examples of bivariate extremal distributions when the margins follow the first asymptotic distribution of the largest values. The variables are assumed to be reduced and each distribution contains only one parameter indicating the association between the extremes. The probability and the density functions of these distributions at the characteristic value, median, and mode have been analyzed. A procedure has been developed to estimate the single parameter of the distributions. A criterion for distinguishing between the two bivariate extremal distributions has been worked out. Finally, the various theories developed are applied to a numerical example.
Gumbel et al. (Thu,) studied this question.