Random Summation

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Random Summation

Author : Boris V. Gnedenko
Publisher : CRC Press
ISBN 13 : 9780849328756
Total Pages : 282 pages
Book Rating : 4.3/5 (287 download)

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Book Synopsis Random Summation by : Boris V. Gnedenko

Download or read book Random Summation written by Boris V. Gnedenko and published by CRC Press. This book was released on 1996-03-27 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.

Random Summation

Author : Boris V. Gnedenko
Publisher : CRC Press
ISBN 13 : 100010267X
Total Pages : 280 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Random Summation by : Boris V. Gnedenko

Download or read book Random Summation written by Boris V. Gnedenko and published by CRC Press. This book was released on 2020-07-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.

Modern Theory of Summation of Random Variables

Author : Vladimir M. Zolotarev
Publisher : Walter de Gruyter
ISBN 13 : 3110936534
Total Pages : 429 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Modern Theory of Summation of Random Variables by : Vladimir M. Zolotarev

Download or read book Modern Theory of Summation of Random Variables written by Vladimir M. Zolotarev and published by Walter de Gruyter. This book was released on 2011-09-06 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is devoted to the publication of high-level monographs and surveys which cover the whole spectrum of probability and statistics. The books of the series are addressed to both experts and advanced students.

Sums of Independent Random Variables

Author : V.V. Petrov
Publisher : Springer Science & Business Media
ISBN 13 : 3642658091
Total Pages : 360 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Sums of Independent Random Variables by : V.V. Petrov

Download or read book Sums of Independent Random Variables written by V.V. Petrov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classic "Limit Dislribntions fOT slt1ns of Independent Ramdorn Vari ables" by B.V. Gnedenko and A.N. Kolmogorov was published in 1949. Since then the theory of summation of independent variables has devel oped rapidly. Today a summing-up of the studies in this area, and their results, would require many volumes. The monograph by I.A. Ibragi mov and Yu. V. I~innik, "Independent and Stationarily Connected VaTiables", which appeared in 1965, contains an exposition of the contem porary state of the theory of the summation of independent identically distributed random variables. The present book borders on that of Ibragimov and Linnik, sharing only a few common areas. Its main focus is on sums of independent but not necessarily identically distri buted random variables. It nevertheless includes a number of the most recent results relating to sums of independent and identically distributed variables. Together with limit theorems, it presents many probahilistic inequalities for sums of an arbitrary number of independent variables. The last two chapters deal with the laws of large numbers and the law of the iterated logarithm. These questions were not treated in Ibragimov and Linnik; Gnedenko and KolmogoTOv deals only with theorems on the weak law of large numbers. Thus this book may be taken as complementary to the book by Ibragimov and Linnik. I do not, however, assume that the reader is familiar with the latter, nor with the monograph by Gnedenko and Kolmogorov, which has long since become a bibliographical rarity

Random Summation

Author : Boris V. Gnedenko
Publisher : CRC Press
ISBN 13 : 1000141179
Total Pages : 282 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Random Summation by : Boris V. Gnedenko

Download or read book Random Summation written by Boris V. Gnedenko and published by CRC Press. This book was released on 2020-07-24 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the asymptotic theory of random summation, combining a strict exposition of the foundations of this theory and recent results. It also includes a description of its applications to solving practical problems in hardware and software reliability, insurance, finance, and more. The authors show how practice interacts with theory, and how new mathematical formulations of problems appear and develop. Attention is mainly focused on transfer theorems, description of the classes of limit laws, and criteria for convergence of distributions of sums for a random number of random variables. Theoretical background is given for the choice of approximations for the distribution of stock prices or surplus processes. General mathematical theory of reliability growth of modified systems, including software, is presented. Special sections deal with doubling with repair, rarefaction of renewal processes, limit theorems for supercritical Galton-Watson processes, information properties of probability distributions, and asymptotic behavior of doubly stochastic Poisson processes. Random Summation: Limit Theorems and Applications will be of use to specialists and students in probability theory, mathematical statistics, and stochastic processes, as well as to financial mathematicians, actuaries, and to engineers desiring to improve probability models for solving practical problems and for finding new approaches to the construction of mathematical models.

The Collected Works of Wassily Hoeffding

Author : Wassily Hoeffding
Publisher : Springer Science & Business Media
ISBN 13 : 1461208653
Total Pages : 653 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis The Collected Works of Wassily Hoeffding by : Wassily Hoeffding

Download or read book The Collected Works of Wassily Hoeffding written by Wassily Hoeffding and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 653 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been a rare privilege to assemble this volume of Wassily Hoeffding's Collected Works. Wassily was, variously, a teacher, supervisor and colleague to us, and his work has had a profound influence on our own. Yet this would not be sufficient reason to publish his collected works. The additional and overwhelmingly compelling justification comes from the fun damental nature of his contributions to Statistics and Probability. Not only were his ideas original, and far-reaching in their implications; Wassily de veloped them so completely and elegantly in his papers that they are still cited as prime references up to half a century later. However, three of his earliest papers are cited rarely, if ever. These include material from his doctoral dissertation. They were written in German, and two of them were published in relatively obscure series. Rather than reprint the original articles, we have chosen to have them translated into English. These trans lations appear in this book, making Wassily's earliest research available to a wide audience for the first time. All other articles (including those of his contributions to Mathematical Reviews which go beyond a simple reporting of contents of articles) have been reproduced as they appeared, together with annotations and corrections made by Wassily on some private copies of his papers. Preceding these articles are three review papers which dis cuss the . impact of his work in some of the areas where he made major contributions.

Random Sums and Branching Stochastic Processes

Author : Ibrahim Rahimov
Publisher : Springer Science & Business Media
ISBN 13 : 1461242169
Total Pages : 207 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Random Sums and Branching Stochastic Processes by : Ibrahim Rahimov

Download or read book Random Sums and Branching Stochastic Processes written by Ibrahim Rahimov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Probability

Author : David F. Anderson
Publisher : Cambridge University Press
ISBN 13 : 110824498X
Total Pages : 447 pages
Book Rating : 4.1/5 (82 download)

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Book Synopsis Introduction to Probability by : David F. Anderson

Download or read book Introduction to Probability written by David F. Anderson and published by Cambridge University Press. This book was released on 2017-11-02 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classroom-tested textbook is an introduction to probability theory, with the right balance between mathematical precision, probabilistic intuition, and concrete applications. Introduction to Probability covers the material precisely, while avoiding excessive technical details. After introducing the basic vocabulary of randomness, including events, probabilities, and random variables, the text offers the reader a first glimpse of the major theorems of the subject: the law of large numbers and the central limit theorem. The important probability distributions are introduced organically as they arise from applications. The discrete and continuous sides of probability are treated together to emphasize their similarities. Intended for students with a calculus background, the text teaches not only the nuts and bolts of probability theory and how to solve specific problems, but also why the methods of solution work.

On the convergence of $\sum c_kf(n_kx)$

$Download On the convergence of $\sum c_kf(n_kx)$ PDF Online Free$

Author : Istvan Berkes
Publisher : American Mathematical Soc.
ISBN 13 : 0821843249
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis On the convergence of $\sum c_kf(n_kx)$ by : Istvan Berkes

Download or read book On the convergence of $\sum c_kf(n_kx)$ written by Istvan Berkes and published by American Mathematical Soc.. This book was released on 2009 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a general study of the convergence problem and intends to prove several fresh results and improve a number of old results in the field. This title studies the case when the nk are random and investigates the discrepancy the sequence (nkx) mod 1.

The Distribution and Properties of a Weighted Sum of Chi Squares

Author : A. H. Feiveson
Publisher :
ISBN 13 :
Total Pages : 52 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis The Distribution and Properties of a Weighted Sum of Chi Squares by : A. H. Feiveson

Download or read book The Distribution and Properties of a Weighted Sum of Chi Squares written by A. H. Feiveson and published by . This book was released on 1968 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Road to Randomness in Physical Systems

Author : Eduardo Engel
Publisher : Springer Science & Business Media
ISBN 13 : 9780387977409
Total Pages : 172 pages
Book Rating : 4.9/5 (774 download)

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Book Synopsis A Road to Randomness in Physical Systems by : Eduardo Engel

Download or read book A Road to Randomness in Physical Systems written by Eduardo Engel and published by Springer Science & Business Media. This book was released on 1992-02-21 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many ways of introducing the concept of probability in classical, deterministic physics. This volume is concerned with one approach, known as 'the method of arbitrary functions', which was first considered by Poincare. Essentially, the method proceeds by associating some uncertainty to our knowledge of both the initial conditions and the values of the physical constants that characterize the evolution of a physical system. By modeling this uncertainty by a probability density distribution, it is then possible to analyze how the state of the system evolves through time. This approach may be applied to a wide variety of classical problems and the author considers here examples as diverse as bouncing balls, simple and coupled harmonic oscillators, integrable systems (such as spinning tops), planetary motion, and billiards. An important aspect of this account is to study the speed of convergence for solutions in order to determine the practical relevance of the method of arbitrary functions for specific examples. Consequently, both new results on convergence, and tractable upper bounds are derived and applied.

The Sum of Us

Author : Heather McGhee
Publisher : One World
ISBN 13 : 0525509577
Total Pages : 450 pages
Book Rating : 4.5/5 (255 download)

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Book Synopsis The Sum of Us by : Heather McGhee

Download or read book The Sum of Us written by Heather McGhee and published by One World. This book was released on 2021-02-16 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: NEW YORK TIMES BESTSELLER • LONGLISTED FOR THE NATIONAL BOOK AWARD • One of today’s most insightful and influential thinkers offers a powerful exploration of inequality and the lesson that generations of Americans have failed to learn: Racism has a cost for everyone—not just for people of color. WINNER OF THE PORCHLIGHT BUSINESS BOOK AWARD • ONE OF THE BEST BOOKS OF THE YEAR: Time, The Washington Post, St. Louis Post-Dispatch, Ms. magazine, BookRiot, Library Journal “This is the book I’ve been waiting for.”—Ibram X. Kendi, #1 New York Times bestselling author of How to Be an Antiracist Look for the author’s new podcast, The Sum of Us, based on this book! Heather McGhee’s specialty is the American economy—and the mystery of why it so often fails the American public. From the financial crisis of 2008 to rising student debt to collapsing public infrastructure, she found a root problem: racism in our politics and policymaking. But not just in the most obvious indignities for people of color. Racism has costs for white people, too. It is the common denominator of our most vexing public problems, the core dysfunction of our democracy and constitutive of the spiritual and moral crises that grip us all. But how did this happen? And is there a way out? McGhee embarks on a deeply personal journey across the country from Maine to Mississippi to California, tallying what we lose when we buy into the zero-sum paradigm—the idea that progress for some of us must come at the expense of others. Along the way, she meets white people who confide in her about losing their homes, their dreams, and their shot at better jobs to the toxic mix of American racism and greed. This is the story of how public goods in this country—from parks and pools to functioning schools—have become private luxuries; of how unions collapsed, wages stagnated, and inequality increased; and of how this country, unique among the world’s advanced economies, has thwarted universal healthcare. But in unlikely places of worship and work, McGhee finds proof of what she calls the Solidarity Dividend: the benefits we gain when people come together across race to accomplish what we simply can’t do on our own. The Sum of Us is not only a brilliant analysis of how we arrived here but also a heartfelt message, delivered with startling empathy, from a black woman to a multiracial America. It leaves us with a new vision for a future in which we finally realize that life can be more than a zero-sum game. LONGLISTED FOR THE ANDREW CARNEGIE MEDAL

Introductory Statistics

Author : Openstax
Publisher :
ISBN 13 : 9788565775120
Total Pages : 914 pages
Book Rating : 4.7/5 (751 download)

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Book Synopsis Introductory Statistics by : Openstax

Download or read book Introductory Statistics written by Openstax and published by . This book was released on 2022-03-23 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. Senior Contributing Authors Barbara Illowsky, De Anza College Susan Dean, De Anza College Contributing Authors Daniel Birmajer, Nazareth College Bryan Blount, Kentucky Wesleyan College Sheri Boyd, Rollins College Matthew Einsohn, Prescott College James Helmreich, Marist College Lynette Kenyon, Collin County Community College Sheldon Lee, Viterbo University Jeff Taub, Maine Maritime Academy

Two-Person Zero-Sum Games

Author : Alan Washburn
Publisher : Springer Science & Business Media
ISBN 13 : 1461490502
Total Pages : 207 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Two-Person Zero-Sum Games by : Alan Washburn

Download or read book Two-Person Zero-Sum Games written by Alan Washburn and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two-person zero-sum game theory deals with situations that are perfectly competitive—there are exactly two decision makers for whom there is no possibility of cooperation or compromise. It is the most fundamental part of game theory, and the part most commonly applied. There are diverse applications to military battles, sports, parlor games, economics and politics. The theory was born in World War II, and has by now matured into a significant and tractable body of knowledge about competitive decision making. The advent of modern, powerful computers has enabled the solution of many games that were once beyond computational reach. Two-Person Zero-Sum Games, 4th Ed. offers an up-to-date introduction to the subject, especially its computational aspects. Any finite game can be solved by the brute force method of enumerating all possible strategies and then applying linear programming. The trouble is that many interesting games have far too many strategies to enumerate, even with the aid of computers. After introducing ideas, terminology, and the brute force method in the initial chapters, the rest of the book is devoted to classes of games that can be solved without enumerating every strategy. Numerous examples are given, as well as an extensive set of exercises. Many of the exercises are keyed to sheets of an included Excel workbook that can be freely downloaded from the SpringerExtras website. This new edition can be used as either a reference book or as a textbook.

An Introduction to Stochastic Modeling

Author : Howard M. Taylor
Publisher : Academic Press
ISBN 13 : 1483220443
Total Pages : 579 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis An Introduction to Stochastic Modeling by : Howard M. Taylor

Download or read book An Introduction to Stochastic Modeling written by Howard M. Taylor and published by Academic Press. This book was released on 2014-05-10 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Discovering Computer Science

Author : Jessen Havill
Publisher : CRC Press
ISBN 13 : 149878674X
Total Pages : 800 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis Discovering Computer Science by : Jessen Havill

Download or read book Discovering Computer Science written by Jessen Havill and published by CRC Press. This book was released on 2016-07-06 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt: Discovering Computer Science: Interdisciplinary Problems, Principles, and Python Programming introduces computational problem solving as a vehicle of discovery in a wide variety of disciplines. With a principles-oriented introduction to computational thinking, the text provides a broader and deeper introduction to computer science than typical introductory programming books. Organized around interdisciplinary problem domains, rather than programming language features, each chapter guides students through increasingly sophisticated algorithmic and programming techniques. The author uses a spiral approach to introduce Python language features in increasingly complex contexts as the book progresses. The text places programming in the context of fundamental computer science principles, such as abstraction, efficiency, and algorithmic techniques, and offers overviews of fundamental topics that are traditionally put off until later courses. The book includes thirty well-developed independent projects that encourage students to explore questions across disciplinary boundaries. Each is motivated by a problem that students can investigate by developing algorithms and implementing them as Python programs. The book's accompanying website — http://discoverCS.denison.edu — includes sample code and data files, pointers for further exploration, errata, and links to Python language references. Containing over 600 homework exercises and over 300 integrated reflection questions, this textbook is appropriate for a first computer science course for computer science majors, an introductory scientific computing course or, at a slower pace, any introductory computer science course.

The Zero-Sum Society

Author : Lester C Thurow
Publisher : Basic Books
ISBN 13 : 0465011594
Total Pages : 238 pages
Book Rating : 4.4/5 (65 download)

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Book Synopsis The Zero-Sum Society by : Lester C Thurow

Download or read book The Zero-Sum Society written by Lester C Thurow and published by Basic Books. This book was released on 2008-01-04 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written during a period of acute economic stagnation in 1980, The Zero-Sum Society discusses the human implications of economic problem solving. Interpreting macroeconomics as a zero-sum game, Thurow proposes that the American economy will not solve its most trenchant problems-inflation, slow economic growth, the environment-until the political economy can support, in theory and in practice, the idea that certain members of society will have to bear the brunt of taxation and other government-sponsored economic actions. As relevant today as it was twenty years ago, The Zero-Sum Society offers a classic set of recommendations about the best way to balance government stewardship of the economy and the free-market aspirations of upwardly mobile Americans.