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Records. (English) Zbl 0914.60007
Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. New York, NY: Wiley. xx, 312 p. (1998).
This book is intended to be a graduate text for a one-term course on basic results and methods in the record value theory. The material is presented in very clear, well-organized fashion. Each chapter ends with exercises which either illustrate or extend the main ideas of the chapter. The following describes the contents. Chapter 1: Introduction. Chapter 2: Basic distributional results: standard record values processes, record values from the classical model, record values from specific distributions, record times and related statistics, moments of record values, a discrete interlude, geometric results, counting process and \(k\)-records. Chapter 3: Moment relations, bounds and approximations. Chapter 4: Characterizations based on record values. Chapter 5: Statistical inference based on observed record sequences. Chapter 6: General record models: geometrically increasing populations, the \(F^\alpha\) record model, linear drift record model, the Pfeifer model, records from dependent sequences. Chapter 7: Random and point process record models. Chapter 8: Higher dimensional problems.
The book is a welcome addition to the existing literature and will be appreciated by probabilists, statisticians, applied statisticians, meteorologists, hydrologists, market analysts, and sport analysts.

60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60G70 Extreme value theory; extremal stochastic processes
62G30 Order statistics; empirical distribution functions