Cornell’s, Esteva’s, and classical formulations for seismic hazard analysis are theoretically described and mathematically unified by a suitable treatment of the random groundmotion variable. Differences and connections among the schemes are discussed, allowing for a better understanding of the underpinning principles of probabilistic seismic hazard analysis. The classical formulation is equivalent to that by Esteva, and they correspond to a general scheme. Although they are mathematically equivalent, the two formulations each has its own particular approach to express the hazard rate, so results may differ. Cornell’s original scheme is a particular case of classical and Esteva’s formulation. It is also shown that intensity exceedance rates for any index of structural performance or at a particular site can be recursively transformed into exceedance rates of other intensity indexes. Formulations are invariant under such a transformation.