Tropical cyclones are affected by a large number of climatic fac-tors, which translates into complex patterns of occurrence. The variability ofannual metrics of tropical-cyclone activity has been intensively studied, in par-ticular since the sudden activation of the North Atlantic inthe mid 1990’s. Weprovide first a swift overview on previous work by diverse authors about theseannual metrics for the North-Atlantic basin, where the natural variability ofthe phenomenon, the existence of trends, the drawbacks of the records, andthe influence of global warming have been the subject of interesting debates.Next, we present an alternative approach that does not focuson seasonalfeatures but on the characteristics of single events [Corral et al.,Nature Phys.6, 693 (2010)]. It is argued that the individual-storm powerdissipation index(PDI) constitutes a natural way to describe each event, and further, that thePDI statistics yields a robust law for the occurrence of tropical cyclones interms of a power law. In this context, methods of fitting thesedistributionsare discussed.As an important extension to this work we introduce a distribution functionthat models the whole range of the PDI density (excluding incompletenesseffects at the smallest values), the gamma distribution, consisting in a power-law with an exponential decay at the tail. The characteristic scale of this decay,represented by the cutoff parameter, provides very valuableinformation on thefiniteness size of the basin, via the largest values of the PDIs that the basincan sustain. We use the gamma fit to evaluate the influence of sea surfacetemperature (SST) on the occurrence of extreme PDI values, for which we findan increase around 50 % in the values of these basin-wide events for a 0.49◦CSST average difference.Similar findings are observed for the effects of the positive phase of theAtlantic multidecadal oscillation and the number of hurricanes in a season onthe PDI distribution. In the case of the El Ni ̃no Southern oscillation (ENSO),positive and negative values of the multivariate ENSO indexdo not have asignificant effect on the PDI distribution; however, when only extreme valuesof the index are used, it is found that the presence of El Ni ̃nodecreases thePDI of the most extreme hurricanes.