Download or read book The Asymptotic Theory of Extreme Order Statistics written by János Galambos and published by . This book was released on 1987 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Asymptotic Theory of Extreme Order Statistics written by Janos Galambos and published by John Wiley & Sons. This book was released on 1978-05-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discusses the stochastic regularity in extreme behavior, presenting the asymptotic theory of extremes as the number of components making up the extremes increases indefinitely. Determines all limiting distributions under different sets of conditions and fully covering the multivariate extreme value theory. Offers for the first time in book form discussions of multivariate extreme value distributions (with full details), extreme value theory for dependent samples, and the almost sure behavior of extremes, extremes for random sample sizes, records and record times, and inequalities of estimates in the univariate case. Mathematically rigorous yet easily accessible, it is equally suitable for textbook adoption or as a major reference source.
Download or read book The Asymptotic Theory of Extreme Order Statistics written by Lawson McDonald and published by . This book was released on 1978 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximate Distributions of Order Statistics written by Rolf-Dieter Reiss and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.
Download or read book Bivariate Generalized Order Statistics written by M. A. Abd Elgawad and published by LAP Lambert Academic Publishing. This book was released on 2014-10-31 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In Kamps (1995) generalized order statistics (GOS) have been introduced as a unifying theme for several models of ascendingly ordered random variables (rv's). Following Kamps, Burkschat et al. (2003) have introduced the concept of dual generalized order statistics (DGOS) to unify several models that produce ordered rv's. The main aim of this book is to study the limit joint distribution function (df) of any two statistics in a wide subclass of the GOS and DGOS models known as m-GOS and m-DGOS respectively. This subclass contains many important practical models such as ordinary order statistics, order statistics with non-integer sample size, sequential order statistics and upper and lower record values. The limit df's of lower-lower extreme, upper-upper extreme, lower-upper extreme, central-central and lower-lower intermediate m-GOS and m-DGOS are obtained. It is revealed that the convergence of the marginals m-GOS and m-DGOS implies the convergence of the joint df. Moreover, the conditions, under which the asymptotic independence between the two marginals occurs, are derived.
Download or read book Statistical Extremes and Applications written by J. Tiago de Oliveira and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first references to statistical extremes may perhaps be found in the Genesis (The Bible, vol. I): the largest age of Methu'selah and the concrete applications faced by Noah-- the long rain, the large flood, the structural safety of the ark --. But as the pre-history of the area can be considered to last to the first quarter of our century, we can say that Statistical Extremes emer ged in the last half-century. It began with the paper by Dodd in 1923, followed quickly by the papers of Fre-chet in 1927 and Fisher and Tippett in 1928, after by the papers by de Finetti in 1932, by Gumbel in 1935 and by von Mises in 1936, to cite the more relevant; the first complete frame in what regards probabilistic problems is due to Gnedenko in 1943. And by that time Extremes begin to explode not only in what regards applications (floods, breaking strength of materials, gusts of wind, etc. ) but also in areas going from Proba bility to Stochastic Processes, from Multivariate Structures to Statistical Decision. The history, after the first essential steps, can't be written in few pages: the narrow and shallow stream gained momentum and is now a huge river, enlarging at every moment and flooding the margins. Statistical Extremes is, thus, a clear-cut field of Probability and Statistics and a new exploding area for research.
Download or read book The Asymptotic Theory of Extreme Order Statistics written by János Galambos and published by . This book was released on 1987 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Theory of Testing Statistical Hypotheses written by Vladimir E. Bening and published by VSP. This book was released on 2000-01-01 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.
Download or read book A First Course in Order Statistics written by Barry C. Arnold and published by SIAM. This book was released on 2008-09-25 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This updated classic text will aid readers in understanding much of the current literature on order statistics: a flourishing field of study that is essential for any practising statistician and a vital part of the training for students in statistics. Written in a simple style that requires no advanced mathematical or statistical background, the book introduces the general theory of order statistics and their applications. The book covers topics such as distribution theory for order statistics from continuous and discrete populations, moment relations, bounds and approximations, order statistics in statistical inference and characterisation results, and basic asymptotic theory. There is also a short introduction to record values and related statistics. The authors have updated the text with suggestions for further reading that may be used for self-study. Written for advanced undergraduate and graduate students in statistics and mathematics, practising statisticians, engineers, climatologists, economists, and biologists.
Download or read book A Course in Large Sample Theory written by Thomas S. Ferguson and published by Routledge. This book was released on 2017-09-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study.
Download or read book Order Statistics written by Herbert A. David and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones.
Download or read book Asymptotic Theory of Order Statistics Under Power Normalization written by Haroon Barakat and published by LAP Lambert Academic Publishing. This book was released on 2012-08 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last two decades E. Pancheva and her collaborators were investigating various limit theorems for extremes using a wider class of normalizing mapping than the linear ones to get a wider class of limit laws. This wider class of extreme limits can be used in solving approximation problems. For extreme order statistics, in a recent paper by Sreehari (2009), the domains of attraction for general nonlinear normalizations are fully characterized, including the question of how to choose suitable norming functions from the knowledge of the sample distribution. The main aim of this thesis is to extend the work of Pancheva (1984) and Sreehari (2009) for the maximum order statistics to order statistics with variable ranks. It is shown that, in contrast to the case of extremes, the well known limit distributions for central order statistics under linear normalization (c.f Smirnov 1952) coincides with those under power normalization. In the case of intermediate order statistics all possible limit distributions under power normalization are derived from corresponding results in the extremal case. Furthermore, the corresponding domains of attractions of these possible limits are derived.
Download or read book Asymptotic Theory of Statistics and Probability written by Anirban DasGupta and published by Springer Science & Business Media. This book was released on 2008-03-07 with total page 726 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.
Download or read book Statistics of Extremes written by E. J. Gumbel and published by Courier Corporation. This book was released on 2012-04-27 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text covers order statistics and their exceedances; exact distribution of extremes; the 1st asymptotic distribution; uses of the 1st, 2nd, and 3rd asymptotes; more. 1958 edition. Includes 44 tables and 97 graphs.
Download or read book Prediction of Component Survival Time by Application of the Asymptotic Theory of Extreme Order Statistics written by Mohamed Gabr Abdallah and published by . This book was released on 1982 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Concept of Generalized Order Statistics written by Udo Kamps and published by Teubner Skripten zur Mathematischen Stochastik. This book was released on 1995 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Order statistics and record values appear in many statistical applications and are widely used in statistical modeling and inference. Both models describe random variables arranged in order of magnitude. In addition to these well-known models, several other models of ordered random variables, known and new ones, are introduced in this book such as order statistics with non-integral sample size, sequential order statistics, k-th record values, Pfeifer' s record model, k -records from non-identical distributions and ordered random variables which arise from n truncation of distributions. These models can be effectively applied, e.g., in reliability theory. Here, an order statistic represents the life-length of some r-out-of-n-system which is an important technical structure consisting of n components. For this application, a new and more adequate model is naturally suggested. Sequential order statistics serve as a model describing certain dependencies or interactions among the system components caused by failures of components. Record values are closely connected with the occurrence times of some corresponding non-homogeneaus Poisson process and used in so lled shock models. More flexible record models, and therefore more applicable to practical situations, are considered here. The main purpose of this book is to present a concept of generalized order statistics as a unified approach to a variety of models of ordered random variables. In the distribution theoretical sense, all of the models mentioned above are contained in the proposed model of generalized order statistics.
Download or read book A First Course in Asymptotic Theory of Statistics written by T. K. Chandra and published by Alpha Science International, Limited. This book was released on 1999-01-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting with elementary notions of calculus, statistics and probability, the author introduces in this book the basic results of asymptotic theory through intuitive and motivated approaches with excellent exposure to various problems. Many theoretical and numerical examples have been worked out along with results that are not available in other books.
