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
Cycles of the Kings the king they served. This they did in poems that blended the mythological and the historical to a greater or lesser degree. The resulting stories form what has come to be known as the Historical Cycle, or more correctly Cycles, as there are a number of independent groupings. The kings that are included range from the almost entirely mythological Labraid Loingsech, who allegedly became High King of Ireland around 431 BC, to the entirely historical Brian Boru. However, the greatest glory of the Historical Cycle is the "Buile Shuibhne" ("The Frenzy of Sweeney"), a 12th-century tale told in verse and