1650245602

Probability and Statistical Models : Foundations for Problems in Reliability and Financial Mathematics / by Arjun K. Gupta, Wei-Bin Zeng, Yanhong Wu

Zeng, Wei-Bin ; Wu, Yanhong

First

Englisch

Boston : Springer Science+Business Media, LLC, 2010

Online-Ressource (XII, 267p, digital)

Includes bibliographical references and index

Buchausg. u.d.T.: Gupta, Arjun K. *1938-*: Probability and statistical models. - New York, NY [u.a.] : Birkhäuser [u.a.], 2010. - XII, 267 S.

978-0-8176-4987-6

1-280-39114-6 ebk

978-1-280-39114-9 MyiLibrary

Weitere Ausgaben: 978-0-8176-4986-9 (Druckausgabe)

DOI: 10.1007/978-0-8176-4987-6

""Probability and Statistical Models""; ""Preface ""; ""Contents ""; ""1 Preliminaries""; ""1.1 Introduction""; ""1.2 Notations""; ""1.3 Random Variable and Distribution Function""; ""1.4 Mean and Variance""; ""1.5 Joint and Conditional Distributions""; ""1.5.1 Joint Distribution""; ""1.5.2 Independent Sums and Laws""; ""1.5.3 Conditional Distribution and Mean""; ""1.6 Survival Function and Failure Rate""; ""1.6.1 Survival Function and Failure Rate""; ""1.6.2 Mean and Mean Residual Life""; ""1.6.3 Cauchy Functional Equation""; ""Problems""; ""2 Exponential Distribution""; ""2.1 Introduction""

""2.2 Exponential Distribution""""2.3 Characterization of Exponential Distribution""; ""2.3.1 Memoryless Property""; ""2.3.2 Constant Failure Rate Function""; ""2.3.3 Extreme Value Distribution""; ""2.4 Order Statistics and Exponential Distribution""; ""2.4.1 Some Properties of Order Statistics""; ""2.4.2 Characterization Based on Order Statistics""; ""2.4.3 Record Values""; ""2.5 More Applications""; ""Problems""; ""3 Poisson Process""; ""3.1 Poisson Process as a Counting Process""; ""3.2 Characterization of Poisson Processes as Counting Processes""

""3.3 Poisson Process as a Renewal Process""""3.4 Further Properties of Poisson Process""; ""3.4.1 Superposition Process""; ""3.4.2 Decomposition of Poisson Process""; ""3.5 Examples of Poisson Process""; ""Problems""; ""4 Parametric Families of Lifetime Distributions""; ""4.1 Weibull Distribution""; ""4.2 Gamma Distribution""; ""4.3 Change-Point Model""; ""4.4 Mixture Exponential Distribution""; ""4.5 IFR (DFR) and Mixture Erlang Distribution""; ""Problems""; ""5 Lifetime Distribution Classes""; ""5.1 IFR and DFR""; ""5.1.1 IFR and PF2""; ""5.1.2 Smoothness of IFR Distribution""

""5.1.3 A Sufficient Condition""""5.2 IFRA and DFRA Classes""; ""5.3 Several Lifetime Distribution Classes""; ""5.4 Preservation of Lifetime Distributions Under Reliability Operations""; ""5.4.1 Independent Sums""; ""5.4.2 Mixture of Lifetime Distributions""; ""5.5 Shock Models and Lifetime Distribution Classes""; ""5.5.1 IFRA Property of Shock Model""; ""5.5.2 Extension of Cumulative Damage Model""; ""5.5.3 General Cumulative Damage Model""; ""5.5.4 Shock Models Leading to Other Lifetime Distributions""; ""Problems""; ""6 Multivariate Lifetime Distributions""

""6.1 Basic Properties of Bivariate Distributions""""6.2 Bivariate Memoryless Property""; ""6.3 Properties of the BVE""; ""6.4 A Nonfatal Shock Model""; ""6.5 Absolutely Continuous Bivariate Exponential Extensions""; ""Problems""; ""7 Association and Dependence""; ""7.1 Several Concepts of Association""; ""7.2 MTP2 Distribution""; ""7.3 Multivariate Failure Rate and Distribution Class""; ""7.4 Negative Association""; ""Problems""; ""8 Renewal Theory""; ""8.1 Renewal Theorem""; ""8.2 High-Order Approximations and Bounds""; ""8.3 Delayed Renewal Process""; ""8.4 Defective Renewal Process""

""Problems""

*Stochastisches Modell

*Stochastisches Modell

*Finance ; Distribution (Probability theory) ; Economics -- Statistics ; Mathematics ; Engineering mathematics ; Statistics . ; Applied mathematics. ; Probabilities. ; Mathematical models. ; Economics, Mathematical . ; Mathematics ; Finance ; Distribution (Probability theory) ; Economics -- Statistics ; Engineering mathematics

Klassifikation der Library of Congress: QA273.A1-274.9 ; QA274-274.9 ; QA276

Dewey Dezimal-Klassifikation: 519.2; ; 520;

Regensburger Verbund-Klassifikation: QH 237: Q Wirtschaftswissenschaften / QH Mathematik. Statistik. Ökonometrie. Unternehmensforschung / QH 200-QH 254 Statistik / QH 230-QH 239 Theoretische Statistik / Zeitreihenanalyse. Anwendungen stochastischer Prozesse, stochastische Prozesse, stochastische Differentialgleichungen

Book Industry Communication: PBWL

Book Industry Communication: PBT

bisacsh: MAT029000

Mathematics Subject Classification: *60-01

Mathematics Subject Classification: 62-01

Mathematics Subject Classification: 60K10

Mathematics Subject Classification: 91G80

Mathematics Subject Classification: 60K05

Mathematics Subject Classification: 90B25

Preliminaries -- Exponential Distribution -- Poisson Process -- Parametric Families of Lifetime Distributions -- Lifetime Distribution Classes -- Multivariate Lifetime Distributions -- Association and Dependence -- Renewal Theory -- Risk Theory -- Asset Pricing Theory -- Credit Risk Modeling.

With an emphasis on models and techniques, this textbook introduces many of the fundamental concepts of stochastic modeling that are now a vital component of almost every scientific investigation. These models form the basis of well-known parametric lifetime distributions such as exponential, Weibull, and gamma distributions, as well as change-point and mixture models. The authors also consider more general notions of non-parametric lifetime distribution classes. In particular, emphasis is placed on laying the foundation for solving problems in reliability, insurance, finance, and credit risk. Exercises and solutions to selected problems accompany each chapter in order to allow students to explore these foundations. The key subjects covered include: * Exponential distributions and the Poisson process * Parametric lifetime distributions * Non-parametric lifetime distribution classes * Multivariate exponential extensions * Association and dependence * Renewal theory * Problems in reliability, insurance, finance, and credit risk This work differs from traditional probability textbooks in a number of ways. Since no measure theory knowledge is necessary to understand the material and coverage of the central limit theorem and normal theory related topics has been omitted, the work may be used as a single-semester senior undergraduate or first-year graduate textbook as well as in a second course on probability modeling. Many of the chapters that examine central topics in applied probability can be read independently, allowing both instructors and readers extra flexibility in their use of the book. Probability and Statistical Models is for a wide audience including advanced undergraduate and beginning-level graduate students, researchers, and practitioners in mathematics, statistics, engineering, and economics.

https://zbmath.org/?q=an:1215.60001 [Zentralblatt MATH]

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https://doi.org/10.1007/978-0-8176-4987-6 [E-books (Springer)]