Frequency of exceedance any peak exceeding is . Its complement, is the probability of exceedance, the probability that has been exceeded at least once by time . This probability can be useful to estimate whether an extreme event will occur during a specified time period, such as the lifespan of a structure or the duration of an operation. If is small, for example for the frequency of a rare event occurring in a short time period, then Under this assumption, the frequency of exceedance is equal to the probability of exceedance per unit time, , and the probability of exceedance can be computed
Parity of a permutation of formula_1 into disjoint cycles, which can be composed in any order because they commute. A cycle formula_49 involving formula_50 points can always be obtained by composing formula_51 transpositions (2-cycles): so call formula_51 the "size" of the cycle, and observe that, under this definition, transpositions are cycles of size 1. From a decomposition into formula_54 disjoint cycles we can obtain a decomposition of formula_1 into formula_56 transpositions, where formula_57 is the size of the th cycle. The number formula_58 is called the discriminant of formula_1, and can also be computed as if we take care to include the fixed points