  The classical multivariate extreme value theory tries to capture the extremal
dependence between the components under a multivariate domain of attraction
condition and it requires each of the components to be in the domain of
attraction of a univariate extreme value distribution as well. The multivariate
extreme value (MEV) model has a rich theory but has some limitations as it
fails to capture the dependence structure in presence of asymptotic
independence. A different approach to MEV was given by Heffernan and Tawn
(2004), where they examined MEV distributions by conditioning on one of the
components to be extreme. Here we assume one of the components to be in
Frech\'et or Weibull domain of attraction and study the behavior of the product
of the components under this conditional extreme value model.
