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 Time should plunge into. The American fiction writer Anthony Doerr in "The Boston Globe" writes "Penrose has never shied away from including mathematics in his texts, and kudos to his publisher for honoring that wish. That said, the second half of "Cycles of Time" offers some seriously hard sledding"; "If you'll forgive a skiing metaphor, "Cycles of Time" is a black diamond of a book." Cycles of Time Cycles of Time: An Extraordinary New View of the Universe is a science book by mathematical physicist Roger Penrose published by The Bodley Head in 2010. The book outlines Penrose's Conformal Cyclic Cosmology