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We use extreme value theory to estimate the probability of successiveexceedances of a threshold value of a time-series of an observable on severalclasses of chaotic dynamical systems. The observables have either a Fr\'echet(fat-tailed) or Weibull (bounded) distribution. The motivation for this workwas to give estimates of the probabilities of sustained periods of weatheranomalies such as heat-waves, cold spells or prolonged periods of rainfall inclimate models. Our predictions are borne out by numerical simulations and alsoanalysis of rainfall and temperature data.

Runs of Extremes of Observables on Dynamical Systems and Applications