Approximate Distributions Of Order Statistics

Author : Rolf-Dieter Reiss
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 47,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396208

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Approximate Distributions of Order Statistics by Rolf-Dieter Reiss Pdf

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.

Author : Barry C. Arnold,Narayanaswamy Balakrishnan
Publisher : Springer Science & Business Media
Page : 183 pages
File Size : 44,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461236443

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Relations, Bounds and Approximations for Order Statistics by Barry C. Arnold,Narayanaswamy Balakrishnan Pdf

Bounds on moments of order statistics have been of interest since Sir Francis Galton (1902) flrst addressed the problem of fairly dividing flrst and second prize money in a competition. The present compendium of results represents our effort to sort the plethora of results into some semblance of order. We have tried to assign priority for results appropriately. We will cheerfully accept corrections. Omissions of interesting results have inevitably occurred. On this too we await (cheerful) corrections. We are grateful to Peggy Franklin (University of California), Janet Leach, Domenica Calabria and Patsy Chan (McMaster University) who shared the responsibility of typing the manuscript. The flnal form of the manuscript owes much to their skill and patience. Barry C. Arnold Riverside, California U. S. A. N. Balakrishnan Hamilton, Ontario Canada November, 1988 Table of Contents Chapter 1: TIlE DISTRIBUTION OF ORDER STATISTICS Exercises 4 Chapter 2: RECURRENCE RELATIONS AND IDENTITIES FOR ORDER STATISTICS 2. 0. Introduction 5 2. 1. Relations for single moments 6 2. 2. Relations for product moments 9 2. 3. Relations for covariances 13 15 2. 4. Results for symmetric populations 2. 5. Results for normal population 17 20 2. 6. Results for two related populations 2. 7. Results for exchangeable variates 23 25 Exercises Chapter 3: BOUNDS ON EXPECTATIONS OF ORDER STATISTICS 3. 0. Introduction 38 3. 1. Universal bounds in the Li. d. case 38 3. 2. Variations on the Samuelson-Scott theme 43 3. 3.

Author : Barry C. Arnold,N. Balakrishnan,H. N. Nagaraja
Publisher : SIAM
Page : 291 pages
File Size : 45,9 Mb
Release : 2008-09-25
Category : Mathematics
ISBN : 9780898716481

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A First Course in Order Statistics by Barry C. Arnold,N. Balakrishnan,H. N. Nagaraja Pdf

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.

Author : Mohammad Ahsanullah,Valeriĭ Borisovich Nevzorov
Publisher : Nova Publishers
Page : 252 pages
File Size : 44,8 Mb
Release : 2005
Category : Mathematics
ISBN : 1594540713

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Order Statistics by Mohammad Ahsanullah,Valeriĭ Borisovich Nevzorov Pdf

A lot of probabilists and statisticians, as well as actuarial mathematicians, reliability engineers, meteorologists, hydrologists, economists, business and sport analysts, very often deal with order statistics, which plays an important role in various fields of statistics and its applications. The authors suggest an approach to studying order statistics which proposes an active participation of our reader in the studying process. This book enables a reader to check his/her level of understanding of the theory of order statistics. It gives basic formulae (without proof), which are most important in the theory, and presents a lot of examples, which illustrate the theoretical statements.

Author : Herbert A. David,Haikady N. Nagaraja
Publisher : John Wiley & Sons
Page : 482 pages
File Size : 47,9 Mb
Release : 2004-03-22
Category : Mathematics
ISBN : 9780471654018

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Order Statistics by Herbert A. David,Haikady N. Nagaraja Pdf

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.

Author : János Galambos
Publisher : Unknown
Page : 442 pages
File Size : 47,6 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015015723904

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The Asymptotic Theory of Extreme Order Statistics by János Galambos Pdf

Author : N. Balakrishnan,Enrique Castillo,Jose-Maria Sarabia Alegria
Publisher : Springer Science & Business Media
Page : 515 pages
File Size : 42,6 Mb
Release : 2007-10-23
Category : Mathematics
ISBN : 9780817644871

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Advances in Distribution Theory, Order Statistics, and Inference by N. Balakrishnan,Enrique Castillo,Jose-Maria Sarabia Alegria Pdf

The purpose of this book is to honor the fundamental contributions to many different areas of statistics made by Barry Arnold. Distinguished and active researchers highlight some of the recent developments in statistical distribution theory, order statistics and their properties, as well as inferential methods associated with them. Applications to survival analysis, reliability, quality control, and environmental problems are emphasized.

Author : N. Balakrishnan,V.B. Melas,S. Ermakov
Publisher : Springer Science & Business Media
Page : 395 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461213185

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Advances in Stochastic Simulation Methods by N. Balakrishnan,V.B. Melas,S. Ermakov Pdf

This is a volume consisting of selected papers that were presented at the 3rd St. Petersburg Workshop on Simulation held at St. Petersburg, Russia, during June 28-July 3, 1998. The Workshop is a regular international event devoted to mathematical problems of simulation and applied statistics organized by the Department of Stochastic Simulation at St. Petersburg State University in cooperation with INFORMS College on Simulation (USA). Its main purpose is to exchange ideas between researchers from Russia and from the West as well as from other coun tries throughout the World. The 1st Workshop was held during May 24-28, 1994, and the 2nd workshop was held during June 18-21, 1996. The selected proceedings of the 2nd Workshop was published as a special issue of the Journal of Statistical Planning and Inference. Russian mathematical tradition has been formed by such genius as Tchebysh eff, Markov and Kolmogorov whose ideas have formed the basis for contempo rary probabilistic models. However, for many decades now, Russian scholars have been isolated from their colleagues in the West and as a result their mathe matical contributions have not been widely known. One of the primary reasons for these workshops is to bring the contributions of Russian scholars into lime light and we sincerely hope that this volume helps in this specific purpose.

Author : Mohammad Ahsanullah,Valery B Nevzorov,Mohammad Shakil
Publisher : Springer Science & Business Media
Page : 244 pages
File Size : 43,7 Mb
Release : 2013-03-13
Category : Mathematics
ISBN : 9789491216831

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An Introduction to Order Statistics by Mohammad Ahsanullah,Valery B Nevzorov,Mohammad Shakil Pdf

This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.

Author : Muhammad Qaiser Shahbaz,Mohammad Ahsanullah,Saman Hanif Shahbaz,Bander M. Al-Zahrani
Publisher : Springer
Page : 294 pages
File Size : 49,5 Mb
Release : 2016-11-29
Category : Mathematics
ISBN : 9789462392250

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Ordered Random Variables: Theory and Applications by Muhammad Qaiser Shahbaz,Mohammad Ahsanullah,Saman Hanif Shahbaz,Bander M. Al-Zahrani Pdf

Ordered Random Variables have attracted several authors. The basic building block of Ordered Random Variables is Order Statistics which has several applications in extreme value theory and ordered estimation. The general model for ordered random variables, known as Generalized Order Statistics has been introduced relatively recently by Kamps (1995).

Author : Michael Dee Taylor
Publisher : IMS
Page : 390 pages
File Size : 43,8 Mb
Release : 1996
Category : Mathematics
ISBN : 0940600404

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Distributions with Fixed Marginals and Related Topics by Michael Dee Taylor Pdf

Author : H. Leon Harter,N. Balakrishnan
Publisher : CRC Press
Page : 696 pages
File Size : 41,8 Mb
Release : 1996-02-21
Category : Mathematics
ISBN : 084939452X

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CRC Handbook of Tables for the Use of Order Statistics in Estimation by H. Leon Harter,N. Balakrishnan Pdf

The CRC Handbook of Tables for the Use of Order Statistics in Estimation revises and significantly expands upon the well-known Order Statistics and Their Use in Testing and Estimation (Volume 2), published in 1970. It brings together tables relating to order statistics from many important distributions and provides maximum likelihood estimations of their parameters based on complete as well as Type-II censored samples. This practical reference describes in detail the method of computation used to construct the tables and illustrates their usefulness with practical examples. The CRC Handbook of Tables for the Use of Order Statistics in Estimation is easy to use and provides information on order statistics estimation at your fingertips.

Author : Mohammad Ahsanullah
Publisher : Nova Publishers
Page : 220 pages
File Size : 43,5 Mb
Release : 2008
Category : Mathematics
ISBN : 1604561750

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New Developments in Applied Statistics Research by Mohammad Ahsanullah Pdf

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.

Author : Mohammad Ahsanullah
Publisher : Springer
Page : 125 pages
File Size : 47,8 Mb
Release : 2017-04-18
Category : Mathematics
ISBN : 9789462391390

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Characterizations of Univariate Continuous Distributions by Mohammad Ahsanullah Pdf

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.

Author : N. Balakrishnan,A. Clifford Cohen
Publisher : Elsevier
Page : 392 pages
File Size : 54,5 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9781483297491

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Order Statistics & Inference by N. Balakrishnan,A. Clifford Cohen Pdf

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.