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| Author | : Richard Davis |
| Publisher | : |
| Total Pages | : 66 |
| Release | : 1989 |
| Genre | : Distribution (Probability theory) |
| ISBN | : |
| Author | : Richard A. Davis |
| Publisher | : |
| Total Pages | : 28 |
| Release | : 1991 |
| Genre | : |
| ISBN | : |
| Author | : Thomas Mikosch |
| Publisher | : Springer Nature |
| Total Pages | : 768 |
| Release | : |
| Genre | : |
| ISBN | : 3031591569 |
| Author | : M. R. Leadbetter |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 344 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461254493 |
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.
| Author | : Samuel Kotz |
| Publisher | : World Scientific |
| Total Pages | : 195 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 1860944027 |
This important book provides an up-to-date comprehensive and down-to-earth survey of the theory and practice of extreme value distributions OCo one of the most prominent success stories of modern applied probability and statistics. Originated by E J Gumbel in the early forties as a tool for predicting floods, extreme value distributions evolved during the last 50 years into a coherent theory with applications in practically all fields of human endeavor where maximal or minimal values (the so-called extremes) are of relevance. The book is of usefulness both for a beginner with a limited probabilistic background and to expert in the field. Sample Chapter(s). Chapter 1.1: Historical Survey (139 KB). Chapter 1.2: The Three Types of Extreme Value Distributions (146 KB). Chapter 1.3: Limiting Distributions and Domain of Attraction (210 KB). Chapter 1.4: Distribution Function and Moments of Type 1 Distribution (160 KB). Chapter 1.5: Order Statistics, Record Values and Characterizations (175 KB). Contents: Univariate Extreme Value Distributions; Generalized Extreme Value Distributions; Multivariate Extreme Value Distributions. Readership: Applied probabilists, applied statisticians, environmental scientists, climatologists, industrial engineers and management experts."
| Author | : |
| Publisher | : |
| Total Pages | : 1092 |
| Release | : 1989 |
| Genre | : Statistics |
| ISBN | : |
| Author | : |
| Publisher | : |
| Total Pages | : 676 |
| Release | : 1995 |
| Genre | : Mathematical statistics |
| ISBN | : |
The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
| Author | : Florin Avram |
| Publisher | : |
| Total Pages | : 30 |
| Release | : 1987 |
| Genre | : |
| ISBN | : |
Skorohod has shown that the convergence of sums of i.i.d. random variables to an alpha-stable Levy process, with 0
| Author | : T. A. Azlarov |
| Publisher | : Springer |
| Total Pages | : 152 |
| Release | : 1986-05-09 |
| Genre | : Mathematics |
| ISBN | : |
Problems of calculating the reliability of instruments and systems and the development of measures to increase efficiency and reduce operational costs confronted physicists and mathe maticians at the end of the '40's and the beginning of the '50's in connection with the unrelia bility of electro-vacuum instruments used in aviation. Since then steadily increasing demands for the accuracy, reliability and complexity required in electronic equipment have served as a stimulus in the development of the theory of reliability. From 1950 to 1955 Epstein and Sobel [67,68] and Davis [62], in an analysis of statistical data of the operating time of an instrument up to failure, showed that the distribution is exponential in many cases. Consequently, the ex ponential distribution became basic to research associated with experiments on life expectancy. Further research has shown that there are a whole series of problems in reliability theory for which the exponential distribution is inapplicable. However, it can practically always be used as a first approximation. The ease of computational work due to the nice properties of the exponential distribution (for example, the lack of memory property, see Section 1) is also a reason for its frequent use. AB a rule, data on the behavior of the failure rate function are used to test the hypothesis that a given distribution belongs to the class of exponential distributions, and order statistics are used to estimate the parameter of the exponential distribution.
| Author | : Sidney I. Resnick |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 338 |
| Release | : 2008 |
| Genre | : Mathematics |
| ISBN | : 9780387759524 |
This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.
