A statistical analysis of the time‐integrated Dst index is performed over 1958–2007. The tail of the probability distribution of extreme time‐integrated Dst events, which occur during strong geomagnetic storms, can be precisely fitted by a power law function with upper cutoff, apparently not exceeded even by the 1859 Carrington event. This time‐integrated Dst is expected to be a reasonable proxy for maximum densities of MeV electrons in the heart of the outer radiation belt, which are known to pose a serious threat to satellites. During such strong events, a correlation is found between the time‐integrated levels of various physical quantities, such as interplanetary magnetic field Bz, particle energy fluxes measured during injections in the magnetotail, geosynchronous ULF wave index, and geomagnetic activity in the inner magnetosphere, suggesting cumulative effects from successive disturbances.