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Approximate Distributions of Order Statistics

Author: Rolf-Dieter Reiss

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 363

ISBN-13: 1461396204

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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.

Book Synopsis Approximate Distributions of Order Statistics by : Rolf-Dieter Reiss

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.

Approximate Empirical Distributions for the Computation of Nonparametric Statistics

Author: Gerald L. Sievers

Publisher:

Published: 1981

Total Pages: 33

ISBN-13:

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This paper discusses a method of approximating the value of a statistic through the use of a grouped frequency distribution. This is of particular interest for nonparametric statistics based on ranks, on the empirical distribution function or on order statistics since it avoids the process of ordering the data and can be carried out quickly, even for large sample sizes. Bounds on the error of approximation are obtained. When a natural grouping of the data exists, the approximation would be the proper statistic to use in its own right. The Wilcoxon signed-rank statistic is treated in detail and other statistics are considered. An efficient computational algorithm is presented. (Author).

Book Synopsis Approximate Empirical Distributions for the Computation of Nonparametric Statistics by : Gerald L. Sievers

Download or read book Approximate Empirical Distributions for the Computation of Nonparametric Statistics written by Gerald L. Sievers and published by . This book was released on 1981 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses a method of approximating the value of a statistic through the use of a grouped frequency distribution. This is of particular interest for nonparametric statistics based on ranks, on the empirical distribution function or on order statistics since it avoids the process of ordering the data and can be carried out quickly, even for large sample sizes. Bounds on the error of approximation are obtained. When a natural grouping of the data exists, the approximation would be the proper statistic to use in its own right. The Wilcoxon signed-rank statistic is treated in detail and other statistics are considered. An efficient computational algorithm is presented. (Author).

A First Course in Order Statistics

Author: Barry C. Arnold

Publisher: SIAM

Published: 2008-09-25

Total Pages: 291

ISBN-13: 0898716489

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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.

Book Synopsis A First Course in Order Statistics by : Barry C. Arnold

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.

A Concept of Generalized Order Statistics

Author: Udo Kamps

Publisher: Teubner Skripten zur Mathematischen Stochastik

Published: 1995

Total Pages: 220

ISBN-13:

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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.

Book Synopsis A Concept of Generalized Order Statistics by : Udo Kamps

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.

Order Statistics

Author: Herbert A. David

Publisher: John Wiley & Sons

Published: 2004-03-22

Total Pages: 482

ISBN-13: 0471654019

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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.

Book Synopsis Order Statistics by : Herbert A. David

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.

Distributions with Fixed Marginals and Related Topics

Author: Michael Dee Taylor

Publisher: IMS

Published: 1996

Total Pages: 390

ISBN-13: 9780940600409

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Book Synopsis Distributions with Fixed Marginals and Related Topics by : Michael Dee Taylor

Download or read book Distributions with Fixed Marginals and Related Topics written by Michael Dee Taylor and published by IMS. This book was released on 1996 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Normal and Student ́s t Distributions and Their Applications

Author: Mohammad Ahsanullah

Publisher: Springer Science & Business Media

Published: 2014-02-07

Total Pages: 163

ISBN-13: 9462390614

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The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Book Synopsis Normal and Student ́s t Distributions and Their Applications by : Mohammad Ahsanullah

Download or read book Normal and Student ́s t Distributions and Their Applications written by Mohammad Ahsanullah and published by Springer Science & Business Media. This book was released on 2014-02-07 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Order Statistics & Inference

Author: Narayanaswamy Balakrishnan

Publisher: Elsevier

Published: 2014-06-28

Total Pages: 399

ISBN-13: 1483297497

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The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

Book Synopsis Order Statistics & Inference by : Narayanaswamy Balakrishnan

Download or read book Order Statistics & Inference written by Narayanaswamy Balakrishnan and published by Elsevier. This book was released on 2014-06-28 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.

New Developments in Applied Statistics Research

Author: Mohammad Ahsanullah

Publisher: Nova Publishers

Published: 2008

Total Pages: 220

ISBN-13: 9781604561753

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Computers have taken a permanent place in almost every human endeavor in the last 20 years. This infiltration requires a learning process on the part of the people utilising them and realising where and how they can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and many others where the statistical studies are essential before the next step can be taken. This book presents recent research in the field from around the globe.

Book Synopsis New Developments in Applied Statistics Research by : Mohammad Ahsanullah

Download or read book New Developments in Applied Statistics Research written by Mohammad Ahsanullah and published by Nova Publishers. This book was released on 2008 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computers have taken a permanent place in almost every human endeavor in the last 20 years. This infiltration requires a learning process on the part of the people utilising them and realising where and how they can be best used beyond the basic and obvious applications. Statistics is an example of their application in many diverse fields to reach conclusions and make projections never before possible. Beyond this, applied statistics is rapidly becoming not only an instrument, but an integral part of the advance of knowledge. There are many fields such as medicine, biology, weather prediction, military planning, and many others where the statistical studies are essential before the next step can be taken. This book presents recent research in the field from around the globe.

Characterizations of Univariate Continuous Distributions

Author: Mohammad Ahsanullah

Publisher: Springer

Published: 2017-04-18

Total Pages: 130

ISBN-13: 9462391394

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Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.

Book Synopsis Characterizations of Univariate Continuous Distributions by : Mohammad Ahsanullah

Download or read book Characterizations of Univariate Continuous Distributions written by Mohammad Ahsanullah and published by Springer. This book was released on 2017-04-18 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides in an organized manner characterizations of univariate probability distributions with many new results published in this area since the 1978 work of Golambos & Kotz "Characterizations of Probability Distributions" (Springer), together with applications of the theory in model fitting and predictions.