  We use extreme value theory to estimate the probability of successive
exceedances of a threshold value of a time-series of an observable on several
classes of chaotic dynamical systems. The observables have either a Fr\'echet
(fat-tailed) or Weibull (bounded) distribution. The motivation for this work
was to give estimates of the probabilities of sustained periods of weather
anomalies such as heat-waves, cold spells or prolonged periods of rainfall in
climate models. Our predictions are borne out by numerical simulations and also
analysis of rainfall and temperature data.
