Extreme events in bimodal systems

The extreme value statistics of systems possessing a two-hump probability density of the relevant variable, in which the left peak is more pronounced than the right one, is studied. It is shown that systems of this type display a nontrivial transient behavior in the form of anomalous fluctuations around the mean, for certain (finite) ranges of observational time windows. The results are illustrated on independent identically distributed random variables, systems possessing two locally stable states and subjected to additive white noise, and dynamical systems in the regime of deterministic chaos.