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Titlebook: Extremes and Related Properties of Random Sequences and Processes; M. R. Leadbetter,Georg Lindgren,Holger Rootzén Book 1983 Springer-Verla

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B. R. Bannister,D. C. Whiteheade obvious fact that the maximum exceeds u if there is at least one upcrossing of the level . However, the upcrossings have an interest in their own right, and as we shall see here, they also contain considerable information about the local structure of the process. This chapter is devoted to the asy
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https://doi.org/10.1007/978-3-031-79211-3f several adjacent levels.For instance, we know from Theorem 9.3.2 and relation (9.2.3) that for a standard normal process each upcrossing of the high level u = u.; with a probability p = τ*/τ is accompanied by an upcrossing also of the level.asymptotically independently of all other upcrossings of
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https://doi.org/10.1007/978-3-8350-9249-5h stochastic models for the loads and forces acting on the material. Thus it is often assumed that the maximum of several loads follows one of the extreme value distributions for maxima. More important, and also less obvious, is that the strength of a piece of material, such as a strip of paper or g
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https://doi.org/10.1007/978-3-662-63311-3forms for the limiting distribution of maxima in sequences of i.i.d. random variables. In the derivation, the possible limiting distributions are identified with a class having a certain stability property—the so-called . distributions. It is further shown that this class consists precisely of the three families known (loosely) as . three
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Synthesis Lectures on Mechanical Engineeringous results to those of Chapter 4. This will be approached using the properties of upcrossings developed in the previous chapter and will result in the limiting double exponential distribution for the maximum, with the appropriate scale and location normalization similar to that in Chapter 4.
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