On The Asymptotic Generalized Order Statistics And Related Functions

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On the Asymptotic Generalized Order Statistics and Related Functions

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Author : Haroon Barakat
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659303449
Total Pages : 120 pages
Book Rating : 4.3/5 (34 download)

Book Synopsis On the Asymptotic Generalized Order Statistics and Related Functions by : Haroon Barakat

Download or read book On the Asymptotic Generalized Order Statistics and Related Functions written by Haroon Barakat and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Kamps (1995) suggested a new theoretical approach, which is called generalized order statistics (gos). This new model includes ordinary order statistics (oos), sequential order statistics, progressive type II censored order statistics and record values. The concept of gos enables a common approach to structural similarities and analogies. The distributional and inferential properties of oos and record values turn out to remain valid for gos (cf. Cramer and Kamps, 2001). Thus, the concept of gos provides a large class of models with many interesting and useful properties for both the description and the analysis of practical problems. Due to this reason, the question arises whether the general distribution theory of gos as well as their properties can be obtained by analogy with that for oos. The latter has been extensively investigated in the literature, e.g., see, David, 1981. The main purpose of this thesis is to investigate the asymptotic behavior of some important functions of gos, in view of theory of statistics and its applications. Some of these functions are non-linear, e.g., extremal product and extremal quotient and other are linear e.g., range and midrange.

A Concept of Generalized Order Statistics

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Author : Udo Kamps
Publisher : Teubner Skripten zur Mathematischen Stochastik
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.3/5 (91 download)

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.

Bivariate Generalized Order Statistics

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Author : M. A. Abd Elgawad
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783659631467
Total Pages : 128 pages
Book Rating : 4.6/5 (314 download)

Book Synopsis Bivariate Generalized Order Statistics by : M. A. Abd Elgawad

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.

The Asymptotic Theory of Extreme Order Statistics

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Author : Janos Galambos
Publisher : John Wiley & Sons
ISBN 13 :
Total Pages : 392 pages
Book Rating : 4.:/5 (44 download)

Book Synopsis The Asymptotic Theory of Extreme Order Statistics by : Janos Galambos

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.

The Asymptotic Theory of Extreme Order Statistics

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Author : János Galambos
Publisher :
ISBN 13 :
Total Pages : 442 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis The Asymptotic Theory of Extreme Order Statistics by : János Galambos

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:

A First Course in Order Statistics

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Author : Barry C. Arnold
Publisher : SIAM
ISBN 13 : 0898716489
Total Pages : 291 pages
Book Rating : 4.8/5 (987 download)

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.

Asymptotic Statistics

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Author : Manfred Denker
Publisher : Birkhäuser
ISBN 13 : 3034892543
Total Pages : 121 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Asymptotic Statistics by : Manfred Denker

Download or read book Asymptotic Statistics written by Manfred Denker and published by Birkhäuser. This book was released on 2012-12-06 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes are based on lectures presented during the seminar on " Asymptotic Statistics" held at SchloB Reisensburg, Gunzburg, May 29-June 5, 1988. They consist of two parts, the theory of asymptotic expansions in statistics and probabilistic aspects of the asymptotic distribution theory in nonparametric statistics. Our intention is to provide a comprehensive presentation of these two subjects, leading from elementary facts to the advanced theory and recent results. Prospects for further research are also included. We would like to thank all participants for their stimulating discussions and their interest in the subjects, which made lecturing very pleasant. Special thanks are due H. Zimmer for her excellent typing. We would also like to take this opportunity to to express our thanks to the Gesellschaft fur mathematische Forschung and to the Deutsche Mathematiker Vereinigung, especially to Professor G. Fischer, for the opportunity to present these lectures and to the Birkhauser Verlag for the publication of these lecture notes. R. Bhattacharya, M. Denker Part I: Asymptotic Expansions in Statistics Rabi Bhattacharya 11 {sect}1. CRAMER-EDGEWORTH EXPANSIONS Let Q be a probability measure on (IRk, B"), B" denoting the Borel sigmafield on IR". Assume that the s - th absolute moment of Q is finite, (1.1) P. := J II x lis Q(dx)

Asymptotic Behavior of Certain Functions of Order Statistics

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Author : Om Prakash Srivastava
Publisher :
ISBN 13 :
Total Pages : 156 pages
Book Rating : 4.:/5 (844 download)

Book Synopsis Asymptotic Behavior of Certain Functions of Order Statistics by : Om Prakash Srivastava

Download or read book Asymptotic Behavior of Certain Functions of Order Statistics written by Om Prakash Srivastava and published by . This book was released on with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Distributional Approach to Asymptotics

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Author : Ricardo Estrada
Publisher : Springer Science & Business Media
ISBN 13 : 0817681302
Total Pages : 467 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis A Distributional Approach to Asymptotics by : Ricardo Estrada

Download or read book A Distributional Approach to Asymptotics written by Ricardo Estrada and published by Springer Science & Business Media. This book was released on 2012-09-08 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...The authors of this remarkable book are among the very few who have faced up to the challenge of explaining what an asymptotic expansion is, and of systematizing the handling of asymptotic series. The idea of using distributions is an original one, and we recommend that you read the book...[it] should be on your bookshelf if you are at all interested in knowing what an asymptotic series is." -"The Bulletin of Mathematics Books" (Review of the 1st edition) ** "...The book is a valuable one, one that many applied mathematicians may want to buy. The authors are undeniably experts in their field...most of the material has appeared in no other book." -"SIAM News" (Review of the 1st edition) This book is a modern introduction to asymptotic analysis intended not only for mathematicians, but for physicists, engineers, and graduate students as well. Written by two of the leading experts in the field, the text provides readers with a firm grasp of mathematical theory, and at the same time demonstrates applications in areas such as differential equations, quantum mechanics, noncommutative geometry, and number theory. Key features of this significantly expanded and revised second edition: * addition of a new chapter and many new sections * wide range of topics covered, including the Ces.ro behavior of distributions and their connections to asymptotic analysis, the study of time-domain asymptotics, and the use of series of Dirac delta functions to solve boundary value problems * novel approach detailing the interplay between underlying theories of asymptotic analysis and generalized functions * extensive examples and exercises at the end of each chapter * comprehensive bibliography and index This work is an excellent tool for the classroom and an invaluable self-study resource that will stimulate application of asymptotic

Asymptotic Distribution Theory in Generalized Isotonic Regression

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Author : Stanford University. Department of Statistics
Publisher :
ISBN 13 :
Total Pages : 356 pages
Book Rating : 4.F/5 ( download)

Book Synopsis Asymptotic Distribution Theory in Generalized Isotonic Regression by : Stanford University. Department of Statistics

Download or read book Asymptotic Distribution Theory in Generalized Isotonic Regression written by Stanford University. Department of Statistics and published by . This book was released on 1978 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

NBS Special Publication

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Author :
Publisher :
ISBN 13 :
Total Pages : 574 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis NBS Special Publication by :

Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download PDF Online Free

Author :
Publisher : Univ of California Press
ISBN 13 : 0520325877
Total Pages : 774 pages
Book Rating : 4.5/5 (23 download)

Book Synopsis by :

Download or read book written by and published by Univ of California Press. This book was released on with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Asymptotic Methods in Probability and Statistics with Applications

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Author : N. Balakrishnan
Publisher : Springer Science & Business Media
ISBN 13 : 1461202094
Total Pages : 541 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Asymptotic Methods in Probability and Statistics with Applications by : N. Balakrishnan

Download or read book Asymptotic Methods in Probability and Statistics with Applications written by N. Balakrishnan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditions of the 150-year-old St. Petersburg School of Probability and Statis tics had been developed by many prominent scientists including P. L. Cheby chev, A. M. Lyapunov, A. A. Markov, S. N. Bernstein, and Yu. V. Linnik. In 1948, the Chair of Probability and Statistics was established at the Department of Mathematics and Mechanics of the St. Petersburg State University with Yu. V. Linik being its founder and also the first Chair. Nowadays, alumni of this Chair are spread around Russia, Lithuania, France, Germany, Sweden, China, the United States, and Canada. The fiftieth anniversary of this Chair was celebrated by an International Conference, which was held in St. Petersburg from June 24-28, 1998. More than 125 probabilists and statisticians from 18 countries (Azerbaijan, Canada, Finland, France, Germany, Hungary, Israel, Italy, Lithuania, The Netherlands, Norway, Poland, Russia, Taiwan, Turkey, Ukraine, Uzbekistan, and the United States) participated in this International Conference in order to discuss the current state and perspectives of Probability and Mathematical Statistics. The conference was organized jointly by St. Petersburg State University, St. Petersburg branch of Mathematical Institute, and the Euler Institute, and was partially sponsored by the Russian Foundation of Basic Researches. The main theme of the Conference was chosen in the tradition of the St.

Asymptotic Behavior of Generalized Functions

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Author : Stevan Pilipovic
Publisher : World Scientific
ISBN 13 : 9814366854
Total Pages : 309 pages
Book Rating : 4.8/5 (143 download)

Book Synopsis Asymptotic Behavior of Generalized Functions by : Stevan Pilipovic

Download or read book Asymptotic Behavior of Generalized Functions written by Stevan Pilipovic and published by World Scientific. This book was released on 2012 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The asymptotic analysis has obtained new impulses with the general development of various branches of mathematical analysis and their applications. In this book, such impulses originate from the use of slowly varying functions and the asymptotic behavior of generalized functions. The most developed approaches related to generalized functions are those of Vladimirov, Drozhinov and Zavyalov, and that of Kanwal and Estrada. The first approach is followed by the authors of this book and extended in the direction of the S-asymptotics. The second approach OCo of Estrada, Kanwal and Vindas OCo is related to moment asymptotic expansions of generalized functions and the Ces''aro behavior. The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. The book can be used by applied mathematicians, physicists, engineers and others who use classical asymptotic methods and wish to consider non-classical objects (generalized functions) and their asymptotics now in a more advanced setting.

Asymptotic Expansions for General Statistical Models

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Author : Johann Pfanzagl
Publisher : Springer Science & Business Media
ISBN 13 : 1461564794
Total Pages : 515 pages
Book Rating : 4.4/5 (615 download)

Book Synopsis Asymptotic Expansions for General Statistical Models by : Johann Pfanzagl

Download or read book Asymptotic Expansions for General Statistical Models written by Johann Pfanzagl and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.

Pseudo-Regularly Varying Functions and Generalized Renewal Processes

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Author : Valeriĭ V. Buldygin
Publisher : Springer
ISBN 13 : 3319995375
Total Pages : 496 pages
Book Rating : 4.3/5 (199 download)

Book Synopsis Pseudo-Regularly Varying Functions and Generalized Renewal Processes by : Valeriĭ V. Buldygin

Download or read book Pseudo-Regularly Varying Functions and Generalized Renewal Processes written by Valeriĭ V. Buldygin and published by Springer. This book was released on 2018-10-12 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various applications in function analysis concerning Abelian and Tauberian theorems can be studied as well as those in studies of the asymptotic behavior of solutions of stochastic differential equations. The classes of functions that are investigated and used in a probabilistic context extend the well-known Karamata theory of regularly varying functions and thus are also of interest in the theory of functions. The book provides a rigorous treatment of the subject and may serve as an introduction to the field. It is aimed at researchers and students working in probability, the theory of stochastic processes, operations research, mathematical statistics, the theory of functions, analytic number theory and complex analysis, as well as economists with a mathematical background. Readers should have completed introductory courses in analysis and probability theory.

Asymptotic Properties of Linear Functions of Order Statistics and Perturbed Empirical Distribution Functions Evaluated at a Random Point

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Author : Cheun-Der Lea
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.:/5 (135 download)

Book Synopsis Asymptotic Properties of Linear Functions of Order Statistics and Perturbed Empirical Distribution Functions Evaluated at a Random Point by : Cheun-Der Lea

Download or read book Asymptotic Properties of Linear Functions of Order Statistics and Perturbed Empirical Distribution Functions Evaluated at a Random Point written by Cheun-Der Lea and published by . This book was released on 1984 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: