Relations Bounds And Approximations For Order Statistics
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Relations Bounds And Approximations For Order Statistics
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Author : Barry C Arnold
language : en
Publisher:
Release Date : 1989-05-22
Relations Bounds And Approximations For Order Statistics written by Barry C Arnold and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-22 with categories.
Relations Bounds And Approximations For Order Statistics
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Author : Barry C. Arnold
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Relations Bounds And Approximations For Order Statistics written by Barry C. Arnold and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
A First Course In Order Statistics
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Author : Barry C. Arnold
language : en
Publisher: SIAM
Release Date : 2008-09-25
A First Course In Order Statistics written by Barry C. Arnold and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-25 with Mathematics categories.
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.
Sharp Inequalities For Ordered Random Variables In Statistics And Reliability
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Author : Narayanaswamy Balakrishnan
language : en
Publisher: Springer Nature
Release Date : 2024
Sharp Inequalities For Ordered Random Variables In Statistics And Reliability written by Narayanaswamy Balakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Electronic books categories.
Zusammenfassung: The book discusses various inequalities and sharp bounds for the usual order statistics as well as some functions of them. In particular, deterministic bounds, bounds for the case of IID samples from general, symmetric and life distributions, IID samples from shape restricted family of distributions, and samples from finite populations are all discussed in detail. An elaborate numerical evaluation and comparison of various bounds are also presented in order to illustrate their inherent differences as well as their precision. Furthermore, their applications to inference, reliability theory and characterizations are also highlighted. The book provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to order statistics and some important functions of them. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general in nature and therefore could be useful in other areas of Probability and Statistics as well
Handbook Of Tables For Order Statistics From Lognormal Distributions With Applications
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Author : N. Balakrishnan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Handbook Of Tables For Order Statistics From Lognormal Distributions With Applications written by N. Balakrishnan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
Lognormal distributions are one of the most commonly studied models in the sta tistical literature while being most frequently used in the applied literature. The lognormal distributions have been used in problems arising from such diverse fields as hydrology, biology, communication engineering, environmental science, reliability, agriculture, medical science, mechanical engineering, material science, and pharma cology. Though the lognormal distributions have been around from the beginning of this century (see Chapter 1), much of the work concerning inferential methods for the parameters of lognormal distributions has been done in the recent past. Most of these methods of inference, particUlarly those based on censored samples, involve extensive use of numerical methods to solve some nonlinear equations. Order statistics and their moments have been discussed quite extensively in the literature for many distributions. It is very well known that the moments of order statistics can be derived explicitly only in the case of a few distributions such as exponential, uniform, power function, Pareto, and logistic. In most other cases in cluding the lognormal case, they have to be numerically determined. The moments of order statistics from a specific lognormal distribution have been tabulated ear lier. However, the moments of order statistics from general lognormal distributions have not been discussed in the statistical literature until now primarily due to the extreme computational complexity in their numerical determination.
Crc Handbook Of Tables For Order Statistics From Inverse Gaussian Distributions With Applications
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Author : N. Balakrishnan
language : en
Publisher: Routledge
Release Date : 2017-11-22
Crc Handbook Of Tables For Order Statistics From Inverse Gaussian Distributions With Applications written by N. Balakrishnan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
First derived within the context of life-testing, inverse Gaussian distribution has become one of the most important and widely employed distributions, and is often used to model the lifetimes of components. It is also used as a model in many varied applications, including fatigue analysis, economic prediction analysis, and the analysis of extreme events such as rainfall and flood levels. The interesting features and properties of this distribution make it an important and realistic model in a variety of problems across numerous disciplines. Because of the broad range of applications, this handbook will be useful not only to members of the statistical community but will also appeal to applied scientists, engineers, econometricians, and anyone who desires a thorough evaluation of this important topic.
A Road To Randomness In Physical Systems
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Author : Eduardo M.R.A. Engel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Road To Randomness In Physical Systems written by Eduardo M.R.A. Engel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There are many ways of introducing the concept of probability in classical, i. e, deter ministic, physics. This work is concerned with one approach, known as "the method of arbitrary funetionJ. " It was put forward by Poincare in 1896 and developed by Hopf in the 1930's. The idea is the following. There is always some uncertainty in our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. A probability density may be used to describe this uncertainty. For many physical systems, dependence on the initial density washes away with time. Inthese cases, the system's position eventually converges to the same random variable, no matter what density is used to describe initial uncertainty. Hopf's results for the method of arbitrary functions are derived and extended in a unified fashion in these lecture notes. They include his work on dissipative systems subject to weak frictional forces. Most prominent among the problems he considers is his carnival wheel example, which is the first case where a probability distribution cannot be guessed from symmetry or other plausibility considerations, but has to be derived combining the actual physics with the method of arbitrary functions. Examples due to other authors, such as Poincare's law of small planets, Borel's billiards problem and Keller's coin tossing analysis are also studied using this framework. Finally, many new applications are presented.
Causation Prediction And Search
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Author : Peter Spirtes
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Causation Prediction And Search written by Peter Spirtes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is intended for anyone, regardless of discipline, who is interested in the use of statistical methods to help obtain scientific explanations or to predict the outcomes of actions, experiments or policies. Much of G. Udny Yule's work illustrates a vision of statistics whose goal is to investigate when and how causal influences may be reliably inferred, and their comparative strengths estimated, from statistical samples. Yule's enterprise has been largely replaced by Ronald Fisher's conception, in which there is a fundamental cleavage between experimental and non experimental inquiry, and statistics is largely unable to aid in causal inference without randomized experimental trials. Every now and then members of the statistical community express misgivings about this turn of events, and, in our view, rightly so. Our work represents a return to something like Yule's conception of the enterprise of theoretical statistics and its potential practical benefits. If intellectual history in the 20th century had gone otherwise, there might have been a discipline to which our work belongs. As it happens, there is not. We develop material that belongs to statistics, to computer science, and to philosophy; the combination may not be entirely satisfactory for specialists in any of these subjects. We hope it is nonetheless satisfactory for its purpose.
Optimal Sequentially Planned Decision Procedures
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Author : Norbert Schmitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Optimal Sequentially Planned Decision Procedures written by Norbert Schmitz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Learning from experience, making decisions on the basis of the available information, and proceeding step by step to a desired goal are fundamental behavioural qualities of human beings. Nevertheless, it was not until the early 1940's that such a statistical theory - namely Sequential Analysis - was created, which allows us to investigate this kind of behaviour in a precise manner. A. Wald's famous sequential probability ratio test (SPRT; see example (1.8» turned out to have an enormous influence on the development of this theory. On the one hand, Wald's fundamental monograph "Sequential Analysis" ([Wa]*) is essentially centered around this test. On the other hand, important properties of the SPRT - e.g. Bayes optimality, minimax-properties, "uniform" optimality with respect to expected sample sizes - gave rise to the development of a general statistical decision theory. As a conse quence, the SPRT's played a dominating role in the further development of sequential analysis and, more generally, in theoretical statistics.
When Does Bootstrap Work
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Author : Enno Mammen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
When Does Bootstrap Work written by Enno Mammen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.