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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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书目名称Extremes and Related Properties of Random Sequences and Processes
编辑M. R. Leadbetter,Georg Lindgren,Holger Rootzén
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丛书名称Springer Series in Statistics
图书封面Titlebook: Extremes and Related Properties of Random Sequences and Processes;  M. R. Leadbetter,Georg Lindgren,Holger Rootzén Book 1983 Springer-Verla
描述Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
出版日期Book 1983
关键词Extremum; Maxima; Properties; Random variable; Stochastischer Prozess; Zufallsfolge; statistics
版次1
doihttps://doi.org/10.1007/978-1-4612-5449-2
isbn_softcover978-1-4612-5451-5
isbn_ebook978-1-4612-5449-2Series ISSN 0172-7397 Series E-ISSN 2197-568X
issn_series 0172-7397
copyrightSpringer-Verlag New York Inc. 1983
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Book 1983s-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
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https://doi.org/10.1007/978-3-658-07291-9 result is possible for upcrossings when α < 2, it will be seen that Poisson limits may be obtained for the related concept of ε-upcrossings, defined similarly to the e-maxima of Chapter 9.Chapter 13 Extremes of Continuous Parameter Stationary Processes Our primary task in this chapter will be to di
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Convergence of the Point Process of Exceedances, and the Distribution of ,th Largest Maximaons of this theorem yield further results concerning joint distributions of kth largest values. The formal definition and simple properties of point processes which will be needed are given in the appendix.
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Exceedances of Levels and ,th Largest Maxima it will be shown that the exceedances take on a Poisson character as . becomes large. This leads to the limiting distributions for the kth largest values for any . rank . = 1, 2,… (the kth “extreme order statistics”) and to their limiting joint distributions.
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