Arnold B.C., Balakrishnan N., Nagaraja H.N. Records

John Wiley & Sons, 1998. — 312 p. — ISBN: 0471081086, 978-0471081081.The first and only comprehensive guide to modern record theory and its applications.
Although it is often thought of as a special topic in order statistics, records form a unique area, independent of the study of sample extremes. Interest in records has increased steadily over the years since Chandler formulated the theory of records in 1952. Numerous applications of them have been developed in such far-flung fields as meteorology, sports analysis, hydrology, and stock market analysis, to name just a few. And the literature on the subject currently comprises papers and journal articles numbering in the hundreds. Which is why it is so nice to have this book devoted exclusively to this lively area of statistics.
Written by an exceptionally well-qualified author team, Records presents a comprehensive treatment of record theory and its applications in a variety of disciplines. With the help of a multitude of fascinating examples, Professors Arnold, Balakrishnan, and Nagaraja help readers quickly master basic and advanced record value concepts and procedures, from the classical record value model to random and multivariate record models. The book follows a rational textbook format, featuring witty and insightful chapter introductions that help smooth transitions from one topic to another and challenging chapter-end exercises, which expand on the material covered. An extensive bibliography and numerous references throughout the text specify sources for further readings on relevant topics. Records is a valuable professional resource for probabilists and statisticians, in addition to applied statisticians, meteorologists, hydrologists, market analysts, and sports analysts. It also makes an excellent primary text for courses in record theory and a supplement to order statistics courses.Who Cares?, A Road Map
Basic Distributional Results
Standard Record Values Processes, Record Values From the Classical Model, Record Values From Specific Distributions,
Record Times and Related Statistics, Markov Chains, Moments of Record Values, A Discrete Interlude,
Geometric Results, Counting Process and k-Records
Moment Relations, Bounds and Approximations
Exponential Distribution, Weibull Distribution, Gumbel Distribution, Lomax Distribution,
Normal Distribution, Logistic Distribution, Bounds and Approximations, Results for k-Records
Characterizations
Characterizing Properties of Record Values, Families of Distributions, The Exponential Distribution,
Other Continuous Distributions, Geometric-Tail Distributions, Dependence Structures of Record Values and Order Statistics
Inference
Maximum Likelihood Estimation, Best Linear Unbiased Estimation, Best Linear Invariant Estimation,
Interval Estimation and Tests of Hypotheses, Point Prediction, Interval Prediction,
Illustrative Examples, Inference with Records and Inter-Record Times, Distribution-Free Tests in Time-Series Using Records
General Record Models
Geometrically Increasing Populations, The F^a Record Model, Linear Drift Record Model,
The Pfeifer Model, Characterizations, Records From Dependent Sequences
Random and Point Process Record Models
Basic Random Record Model, Basic Point Process Model and Applications, Records Over Poisson Processes,
Records Over a Renewal Process, Records Over Birth Processes, Records Over Other Pacing Processes,
The Secretary Problem
Higher Dimensional Problems
How Should We Define Multivariate Records?, Bivariate Records With Independent Coordinates,
Concomitants of Records, Lower and Upper Records and the Record Range, Records in Partially Ordered Sets