Discrete Q Distributions

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Discrete q-Distributions

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 1119119049
Total Pages : 262 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Discrete q-Distributions by : Charalambos A. Charalambides

Download or read book Discrete q-Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2016-03-07 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained study of the various applications and developments of discrete distribution theory Written by a well-known researcher in the field, Discrete q-Distributions features an organized presentation of discrete q-distributions based on the stochastic model of a sequence of independent Bernoulli trials. In an effort to keep the book self-contained, the author covers all of the necessary basic q-sequences and q-functions. The book begins with an introduction of the notions of a q-power, a q-factorial, and a q-binomial coefficient and proceeds to discuss the basic q-combinatorics and q-hypergeometric series. Next, the book addresses discrete q-distributions with success probability at a trial varying geometrically, with rate q, either with the number of previous trials or with the number of previous successes. Further, the book examines two interesting stochastic models with success probability at any trial varying geometrically both with the number of trials and the number of successes and presents local and global limit theorems. Discrete q-Distributions also features: Discussions of the definitions and theorems that highlight key concepts and results Several worked examples that illustrate the applications of the presented theory Numerous exercises at varying levels of difficulty that consolidate the concepts and results as well as complement, extend, or generalize the results Detailed hints and answers to all the exercises in an appendix to help less-experienced readers gain a better understanding of the content An up-to-date bibliography that includes the latest trends and advances in the field and provides a collective source for further research An Instructor’s Solutions Manual available on a companion website A unique reference for researchers and practitioners in statistics, mathematics, physics, engineering, and other applied sciences, Discrete q-Distributions is also an appropriate textbook for graduate-level courses in discrete statistical distributions, distribution theory, and combinatorics.

Multivariate Discrete q-Distributions

Author : Charalambos A. Charalambides
Publisher : Springer Nature
ISBN 13 : 3031437136
Total Pages : 134 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Multivariate Discrete q-Distributions by : Charalambos A. Charalambides

Download or read book Multivariate Discrete q-Distributions written by Charalambos A. Charalambides and published by Springer Nature. This book was released on 2023-12-24 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of multivariate discrete q-distributions, which is greatly facilitated by existing multivariate q-sequences and q-functions. Classical multivariate discrete distributions are defined on a sequence of independent and identically distributed Bernoulli trials, with either being a success of a certain rank (level) or a failure. The author relaxes the assumption that the probability of success of a trial is constant by assuming that it varies geometrically with the number of trials and/or the number of successes. The latter is advantageous in the sense that it permits incorporating the experience gained from the previous trials and/or successes, which leads to multivariate discrete q-distributions. Furthermore, q-multinomial and negative q-multinomial formulae are obtained. Next, the book addresses q-multinomial and negative q-multinomial distributions of the first and second kind. The author also examines multiple q-Polya urn model, multivariate q-Polya and inverse q-Polya distributions. Presents definitions and theorems that highlight key concepts and worked examples to illustrate the various applications Contains numerous exercises at varying levels of difficulty that consolidate the presented concepts and results Includes hints and answers to all exercises via the appendix and is supplemented with an Instructor's Solution Manual

Discrete q-Distributions

Author : Charalambos A. Charalambides
Publisher : John Wiley & Sons
ISBN 13 : 1119119057
Total Pages : 264 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Discrete q-Distributions by : Charalambos A. Charalambides

Download or read book Discrete q-Distributions written by Charalambos A. Charalambides and published by John Wiley & Sons. This book was released on 2016-03-16 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained study of the various applications and developments of discrete distribution theory Written by a well-known researcher in the field, Discrete q-Distributions features an organized presentation of discrete q-distributions based on the stochastic model of a sequence of independent Bernoulli trials. In an effort to keep the book self-contained, the author covers all of the necessary basic q-sequences and q-functions. The book begins with an introduction of the notions of a q-power, a q-factorial, and a q-binomial coefficient and proceeds to discuss the basic q-combinatorics and q-hypergeometric series. Next, the book addresses discrete q-distributions with success probability at a trial varying geometrically, with rate q, either with the number of previous trials or with the number of previous successes. Further, the book examines two interesting stochastic models with success probability at any trial varying geometrically both with the number of trials and the number of successes and presents local and global limit theorems. Discrete q-Distributions also features: Discussions of the definitions and theorems that highlight key concepts and results Several worked examples that illustrate the applications of the presented theory Numerous exercises at varying levels of difficulty that consolidate the concepts and results as well as complement, extend, or generalize the results Detailed hints and answers to all the exercises in an appendix to help less-experienced readers gain a better understanding of the content An up-to-date bibliography that includes the latest trends and advances in the field and provides a collective source for further research An Instructor’s Solutions Manual available on a companion website A unique reference for researchers and practitioners in statistics, mathematics, physics, engineering, and other applied sciences, Discrete q-Distributions is also an appropriate textbook for graduate-level courses in discrete statistical distributions, distribution theory, and combinatorics.

Univariate Discrete Distributions

Author : Norman L. Johnson
Publisher : John Wiley & Sons
ISBN 13 : 0471715808
Total Pages : 676 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Univariate Discrete Distributions by : Norman L. Johnson

Download or read book Univariate Discrete Distributions written by Norman L. Johnson and published by John Wiley & Sons. This book was released on 2005-10-03 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Set Contains: Continuous Multivariate Distributions, Volume 1, Models and Applications, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 1, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Continuous Univariate Distributions, Volume 2, 2nd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discrete Multivariate Distributions by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Univariate Discrete Distributions, 3rd Edition by Samuel Kotz, N. Balakrishnan and Normal L. Johnson Discover the latest advances in discrete distributions theory The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method. A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions. Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including: Families of discrete distributions Binomial distribution Poisson distribution Negative binomial distribution Hypergeometric distributions Logarithmic and Lagrangian distributions Mixture distributions Stopped-sum distributions Matching, occupancy, runs, and q-series distributions Parametric regression models and miscellanea Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications. With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.

Probability For Dummies

Author : Deborah J. Rumsey
Publisher : John Wiley & Sons
ISBN 13 : 1118429095
Total Pages : 470 pages
Book Rating : 4.1/5 (184 download)

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Book Synopsis Probability For Dummies by : Deborah J. Rumsey

Download or read book Probability For Dummies written by Deborah J. Rumsey and published by John Wiley & Sons. This book was released on 2018-05-25 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: Packed with practical tips and techniques for solving probability problems Increase your chances of acing that probability exam -- or winning at the casino! Whether you're hitting the books for a probability or statistics course or hitting the tables at a casino, working out probabilities can be problematic. This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success! Discover how to * Conquer combinations and permutations * Understand probability models from binomial to exponential * Make good decisions using probability * Play the odds in poker, roulette, and other games

Lattice Path Combinatorics and Applications

Author : George E. Andrews
Publisher : Springer
ISBN 13 : 3030111024
Total Pages : 443 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Lattice Path Combinatorics and Applications by : George E. Andrews

Download or read book Lattice Path Combinatorics and Applications written by George E. Andrews and published by Springer. This book was released on 2019-03-02 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most recent methods in various branches of lattice path and enumerative combinatorics along with relevant applications are nicely grouped together and represented in this research contributed volume. Contributions to this edited volume will be mainly research articles however it will also include several captivating, expository articles (along with pictures) on the life and mathematical work of leading researchers in lattice path combinatorics and beyond. There will be four or five expository articles in memory of Shreeram Shankar Abhyankar and Philippe Flajolet and honoring George Andrews and Lajos Takács. There may be another brief article in memory of Professors Jagdish Narayan Srivastava and Joti Lal Jain. New research results include the kernel method developed by Flajolet and others for counting different classes of lattice paths continues to produce new results in counting lattice paths. The recent investigation of Fishburn numbers has led to interesting counting interpretations and a family of fascinating congruences. Formulas for new methods to obtain the number of Fq-rational points of Schubert varieties in Grassmannians continues to have research interest and will be presented here. Topics to be included are far reaching and will include lattice path enumeration, tilings, bijections between paths and other combinatoric structures, non-intersecting lattice paths, varieties, Young tableaux, partitions, enumerative combinatorics, discrete distributions, applications to queueing theory and other continuous time models, graph theory and applications. Many leading mathematicians who spoke at the conference from which this volume derives, are expected to send contributions including. This volume also presents the stimulating ideas of some exciting newcomers to the Lattice Path Combinatorics Conference series; “The 8th Conference on Lattice Path Combinatorics and Applications” provided opportunities for new collaborations; some of the products of these collaborations will also appear in this book. This book will have interest for researchers in lattice path combinatorics and enumerative combinatorics. This will include subsets of researchers in mathematics, statistics, operations research and computer science. The applications of the material covered in this edited volume extends beyond the primary audience to scholars interested queuing theory, graph theory, tiling, partitions, distributions, etc. An attractive bonus within our book is the collection of special articles describing the top recent researchers in this area of study and documenting the interesting history of who, when and how these beautiful combinatorial results were originally discovered.

Introductory Business Statistics 2e

Author : Alexander Holmes
Publisher :
ISBN 13 :
Total Pages : 1801 pages
Book Rating : 4./5 ( download)

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Book Synopsis Introductory Business Statistics 2e by : Alexander Holmes

Download or read book Introductory Business Statistics 2e written by Alexander Holmes and published by . This book was released on 2023-12-13 with total page 1801 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory Business Statistics 2e aligns with the topics and objectives of the typical one-semester statistics course for business, economics, and related majors. The text provides detailed and supportive explanations and extensive step-by-step walkthroughs. The author places a significant emphasis on the development and practical application of formulas so that students have a deeper understanding of their interpretation and application of data. Problems and exercises are largely centered on business topics, though other applications are provided in order to increase relevance and showcase the critical role of statistics in a number of fields and real-world contexts. The second edition retains the organization of the original text. Based on extensive feedback from adopters and students, the revision focused on improving currency and relevance, particularly in examples and problems. This is an adaptation of Introductory Business Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License.

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.

Maintenance Theory of Reliability

Author : Toshio Nakagawa
Publisher : Springer Science & Business Media
ISBN 13 : 1846282217
Total Pages : 275 pages
Book Rating : 4.8/5 (462 download)

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Book Synopsis Maintenance Theory of Reliability by : Toshio Nakagawa

Download or read book Maintenance Theory of Reliability written by Toshio Nakagawa and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many serious accidents have happened in the world where systems have been large-scale and complex, and have caused heavy damage and a social sense of instability. Furthermore, advanced nations have almost ?nished public inf- structureandrushedintoamaintenanceperiod.Maintenancewillbemore- portant than production, manufacture, and construction, that is, more ma- tenance for environmental considerations and for the protection of natural resources. From now on, the importance of maintenance will increase more and more. In the past four decades, valuable contributions to maintenance policies in reliability theory have been made. This book is intended to s- marize the research results studied mainly by the author in the past three decades. The book deals primarily with standard to advanced problems of main- nance policies for system reliability models. System reliability can be mainly improved by repair and preventive maintenance, and replacement, and rel- bility properties can be investigated by using stochastic process techniques. The optimum maintenance policies for systems that minimize or maximize appropriate objective functions under suitable conditions are discussed both analytically and practically. The book is composed of nine chapters. Chapter 1 is devoted to an int- duction to reliability theory, and brie?y reviews stochastic processes needed for reliability and maintenance theory. Chapter 2 summarizes the results of repair maintenance, which is the most basic maintenance in reliability. The repair maintenance of systems such as the one-unit system and multiple-unit redundant systems is treated. Chapters 3 through 5 summarize the results of three typical maintenance policies of age, periodic, and block replacements.

Advances on Models, Characterizations and Applications

Author : N. Balakrishnan
Publisher : CRC Press
ISBN 13 : 1420028693
Total Pages : 253 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Advances on Models, Characterizations and Applications by : N. Balakrishnan

Download or read book Advances on Models, Characterizations and Applications written by N. Balakrishnan and published by CRC Press. This book was released on 2005-05-31 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Statistical distributions are one of the most important applied mathematical tools across a wide spectrum of disciplines, including engineering, biological sciences, and health and social sciences. Since they are used to model observed data and ultimately to develop inferential procedures, understanding the properties of statistical distributions i

Lifetime Analysis by Aging Intensity Functions

Author : Magdalena Szymkowiak
Publisher : Springer
ISBN 13 : 3030121070
Total Pages : 224 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Lifetime Analysis by Aging Intensity Functions by : Magdalena Szymkowiak

Download or read book Lifetime Analysis by Aging Intensity Functions written by Magdalena Szymkowiak and published by Springer. This book was released on 2019-02-01 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a range of aging intensity functions, which make it possible to measure and compare aging trends for lifetime random variables. Moreover, they can be used for the characterization of lifetime distributions, also with bounded support. Stochastic orders based on the aging intensities, and their connections with some other orders, are also discussed. To demonstrate the applicability of aging intensity in reliability practice, the book analyzes both real and generated data. The estimated, properly chosen, aging intensity function is mainly recommended to identify data’s lifetime distribution, and secondly, to estimate some of the parameters of the identified distribution. Both reliability researchers and practitioners will find the book a valuable guide and source of inspiration.

Hypergeometric Orthogonal Polynomials and Their q-Analogues

Author : Roelof Koekoek
Publisher : Springer Science & Business Media
ISBN 13 : 364205014X
Total Pages : 584 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Hypergeometric Orthogonal Polynomials and Their q-Analogues by : Roelof Koekoek

Download or read book Hypergeometric Orthogonal Polynomials and Their q-Analogues written by Roelof Koekoek and published by Springer Science & Business Media. This book was released on 2010-03-18 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively. The fa- lies of orthogonal polynomials in these two schemes generalize the classical orth- onal polynomials (Jacobi, Laguerre and Hermite polynomials) and they have pr- erties similar to them. In fact, they have properties so similar that I am inclined (f- lowing Andrews & Askey [34]) to call all families in the (q-)Askey scheme classical orthogonal polynomials, and to call the Jacobi, Laguerre and Hermite polynomials very classical orthogonal polynomials. These very classical orthogonal polynomials are good friends of mine since - most the beginning of my mathematical career. When I was a fresh PhD student at the Mathematical Centre (now CWI) in Amsterdam, Dick Askey spent a sabbatical there during the academic year 1969–1970. He lectured to us in a very stimulating wayabouthypergeometricfunctionsandclassicalorthogonalpolynomials. Evenb- ter, he gave us problems to solve which might be worth a PhD. He also pointed out to us that there was more than just Jacobi, Laguerre and Hermite polynomials, for instance Hahn polynomials, and that it was one of the merits of the Higher Transc- dental Functions (Bateman project) that it included some newer stuff like the Hahn polynomials (see [198, §10. 23]).

Fractional System Identification

Author : Tom T. Hartley
Publisher :
ISBN 13 :
Total Pages : 22 pages
Book Rating : 4.:/5 (317 download)

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Book Synopsis Fractional System Identification by : Tom T. Hartley

Download or read book Fractional System Identification written by Tom T. Hartley and published by . This book was released on 1999 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper discusses the identification of fractional- and integer-order systems using the concept of continuous order-distribution. Based on the ability to define systems using continuous order-distributions, it is shown that frequency domain system identification can be performed using least squares techniques after discretizing the order-distribution.

Distributions With Given Marginals and Statistical Modelling

Author : Carles M. Cuadras
Publisher : Springer Science & Business Media
ISBN 13 : 9401700613
Total Pages : 252 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Distributions With Given Marginals and Statistical Modelling by : Carles M. Cuadras

Download or read book Distributions With Given Marginals and Statistical Modelling written by Carles M. Cuadras and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers presented at the meeting "Distributions with given marginals and statistical modelling", held in Barcelona (Spain), July 17- 20, 2000. This is the fourth meeting on given marginals, showing that this topic has aremarkable interest. BRIEF HISTORY The construction of distributions with given marginals started with the seminal papers by Hoeffding (1940) and Fn!chet (1951). Since then, many others have contributed on this topic: Dall' Aglio, Farlie, Gumbel, Johnson, Kellerer, Kotz, Morgenstern, Marshali, Olkin, Strassen, Vitale, Whitt, etc., as weIl as Arnold, Cambanis, Deheuvels, Genest, Frank, Joe, Kirneldorf, Nelsen, Rüschendorf, Sampson, Scarsini, Tiit, etc. In 1957 Sklar and Schweizer introduced probabilistic metric spaces. In 1975 Kirneldorf and Sampson studied the uniform representation of a bivariate dis tribution and proposed the desirable conditions that should be satisfied by any bivariate family. In 1991 Darsow, Nguyen and Olsen defined a natural operation between cop ulas, with applications in stochastic processes. In 1993, AIsina, Nelsen and Schweizer introduced the notion of quasi-copula

Polynomials

Author : Ákos Pintér
Publisher : MDPI
ISBN 13 : 303650818X
Total Pages : 154 pages
Book Rating : 4.0/5 (365 download)

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Book Synopsis Polynomials by : Ákos Pintér

Download or read book Polynomials written by Ákos Pintér and published by MDPI. This book was released on 2021-09-03 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: Polynomials play a crucial role in many areas of mathematics including algebra, analysis, number theory, and probability theory. They also appear in physics, chemistry, and economics. Especially extensively studied are certain infinite families of polynomials. Here, we only mention some examples: Bernoulli, Euler, Gegenbauer, trigonometric, and orthogonal polynomials and their generalizations. There are several approaches to these classical mathematical objects. This Special Issue presents nine high quality research papers by leading researchers in this field. I hope the reading of this work will be useful for the new generation of mathematicians and for experienced researchers as well.

Handbook of Mathematical Statistics

Author : Henry Lewis Rietz
Publisher :
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.:/5 (9 download)

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Book Synopsis Handbook of Mathematical Statistics by : Henry Lewis Rietz

Download or read book Handbook of Mathematical Statistics written by Henry Lewis Rietz and published by . This book was released on 1924 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Machine Learning and Big Data Analytics Paradigms: Analysis, Applications and Challenges

Author : Aboul Ella Hassanien
Publisher : Springer Nature
ISBN 13 : 303059338X
Total Pages : 648 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Machine Learning and Big Data Analytics Paradigms: Analysis, Applications and Challenges by : Aboul Ella Hassanien

Download or read book Machine Learning and Big Data Analytics Paradigms: Analysis, Applications and Challenges written by Aboul Ella Hassanien and published by Springer Nature. This book was released on 2020-12-14 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present the state of the art in research on machine learning and big data analytics. The accepted chapters covered many themes including artificial intelligence and data mining applications, machine learning and applications, deep learning technology for big data analytics, and modeling, simulation, and security with big data. It is a valuable resource for researchers in the area of big data analytics and its applications.