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Author: Barry C. Arnold
Publisher: Springer Science & Business Media
ISBN: 1461236444
Category : Mathematics
Languages : en
Pages : 183
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Book Description
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
Publisher: Springer Science & Business Media
ISBN: 1461236444
Category : Mathematics
Languages : en
Pages : 183
Get Book Here
Book Description
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
Publisher:
ISBN: 9781461236450
Category :
Languages : en
Pages : 188
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Book Description
Author: Barry C. Arnold
Publisher: SIAM
ISBN: 0898716489
Category : Mathematics
Languages : en
Pages : 291
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Book Description
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: Sergey Bobkov
Publisher: American Mathematical Soc.
ISBN: 1470436507
Category : Education
Languages : en
Pages : 126
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Book Description
This work is devoted to the study of rates of convergence of the empirical measures μn=1n∑nk=1δXk, n≥1, over a sample (Xk)k≥1 of independent identically distributed real-valued random variables towards the common distribution μ in Kantorovich transport distances Wp. The focus is on finite range bounds on the expected Kantorovich distances E(Wp(μn,μ)) or [E(Wpp(μn,μ))]1/p in terms of moments and analytic conditions on the measure μ and its distribution function. The study describes a variety of rates, from the standard one 1n√ to slower rates, and both lower and upper-bounds on E(Wp(μn,μ)) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.
Author: Roman Vershynin
Publisher: Cambridge University Press
ISBN: 1108415199
Category : Business & Economics
Languages : en
Pages : 299
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Book Description
An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Barry C. Arnold
Publisher: John Wiley & Sons
ISBN: 1118150406
Category : Mathematics
Languages : en
Pages : 342
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Book Description
The first and only comprehensive guide to modern record theory andits applications Although it is often thought of as a special topic in orderstatistics, records form a unique area, independent of the study ofsample extremes. Interest in records has increased steadily overthe years since Chandler formulated the theory of records in 1952.Numerous applications of them have been developed in such far-flungfields as meteorology, sports analysis, hydrology, and stock marketanalysis, to name just a few. And the literature on the subjectcurrently comprises papers and journal articles numbering in thehundreds. Which is why it is so nice to have this book devotedexclusively to this lively area of statistics. Written by an exceptionally well-qualified author team, Recordspresents a comprehensive treatment of record theory and itsapplications in a variety of disciplines. With the help of amultitude of fascinating examples, Professors Arnold, Balakrishnan,and Nagaraja help readers quickly master basic and advanced recordvalue concepts and procedures, from the classical record valuemodel to random and multivariate record models. The book follows arational textbook format, featuring witty and insightful chapterintroductions that help smooth transitions from one topic toanother and challenging chapter-end exercises, which expand on thematerial covered. An extensive bibliography and numerous referencesthroughout the text specify sources for further readings onrelevant topics. Records is a valuable professional resource forprobabilists and statisticians, in addition to appliedstatisticians, meteorologists, hydrologists, market analysts, andsports analysts. It also makes an excellent primary text forcourses in record theory and a supplement to order statisticscourses.
Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 0387217363
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Taken literally, the title "All of Statistics" is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data.
Author: Ibrahim Rahimov
Publisher: Springer Science & Business Media
ISBN: 1461242169
Category : Mathematics
Languages : en
Pages : 207
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Book Description
The aim of this monograph is to show how random sums (that is, the summation of a random number of dependent random variables) may be used to analyse the behaviour of branching stochastic processes. The author shows how these techniques may yield insight and new results when applied to a wide range of branching processes. In particular, processes with reproduction-dependent and non-stationary immigration may be analysed quite simply from this perspective. On the other hand some new characterizations of the branching process without immigration dealing with its genealogical tree can be studied. Readers are assumed to have a firm grounding in probability and stochastic processes, but otherwise this account is self-contained. As a result, researchers and graduate students tackling problems in this area will find this makes a useful contribution to their work.
Author: Shelemyahu Zacks
Publisher: Springer
ISBN: 1461226902
Category : Mathematics
Languages : en
Pages : 188
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Book Description
The present monograph is a comprehensive summary of the research on visibility in random fields, which I have conducted with the late Professor Micha Yadin for over ten years. This research, which resulted in several published papers and technical reports (see bibliography), was motivated by some military problems, which were brought to our attention by Mr. Pete Shugart of the US Army TRADOC Systems Analysis Activity, presently called US Army TRADOC Analysis Command. The Director ofTRASANA at the time, the late Dr. Wilbur Payne, identified the problems and encouraged the support and funding of this research by the US Army. Research contracts were first administered through the Office of Naval Research, and subsequently by the Army Research Office. We are most grateful to all involved for this support and encouragement. In 1986 I administered a three-day workshop on problem solving in the area of sto chastic visibility. This workshop was held at the White Sands Missile Range facility. A set of notes with some software were written for this workshop. This workshop led to the incorporation of some of the methods discussed in the present book into the Army simulation package CASTFOREM. Several people encouraged me to extend those notes and write the present monograph on the level of those notes, so that the material will be more widely available for applications.
Author: Bernard van Cutsem
Publisher: Springer Science & Business Media
ISBN: 1461226864
Category : Mathematics
Languages : en
Pages : 251
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Book Description
Classifying objects according to their likeness seems to have been a step in the human process of acquiring knowledge, and it is certainly a basic part of many of the sciences. Historically, the scientific process has involved classification and organization particularly in sciences such as botany, geology, astronomy, and linguistics. In a modern context, we may view classification as deriving a hierarchical clustering of objects. Thus, classification is close to factorial analysis methods and to multi-dimensional scaling methods. It provides a mathematical underpinning to the analysis of dissimilarities between objects.
