Probability and Statistical Inference

Author: Robert V. Hogg,Elliot A. Tanis

Publisher: Prentice Hall

ISBN: 9780321584755

Category: Mathematics

Page: 622

View: 6818

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BOOK DESCRIPTION: Written by two leading statisticians, this applied introduction to the mathematics of probability and statistics emphasizes the existence of variation in almost every process, and how the study of probability and statistics helps us understand this variation. Designed for students with a background in calculus, this book continues to reinforce basic mathematical concepts with numerous real-world examples and applications to illustrate the relevance of key concepts. NEW TO THIS EDITION: The included CD-ROM contains all of the data sets in a variety of formats for use with most statistical software packages. This disc also includes several applications of Minitab® and Maple(tm). Historical vignettes at the end of each chapter outline the origin of the greatest accomplishments in the field of statistics, adding enrichment to the course. Content updates The first five chapters have been reorganized to cover a standard probability course with more real examples and exercises. These chapters are important for students wishing to pass the first actuarial exam, and cover the necessary material needed for students taking this course at the junior level. Chapters 6 and 7 on estimation and tests of statistical hypotheses tie together confidence intervals and tests, including one-sided ones. There are separate chapters on nonparametric methods, Bayesian methods, and Quality Improvement. Chapters 4 and 5 include a strong discussion on conditional distributions and functions of random variables, including Jacobians of transformations and the moment-generating technique. Approximations of distributions like the binomial and the Poisson with the normal can be found using the central limit theorem. Chapter 8 (Nonparametric Methods) includes most of the standards tests such as those by Wilcoxon and also the use of order statistics in some distribution-free inferences. Chapter 9 (Bayesian Methods) explains the use of the "Dutch book" to prove certain probability theorems. Chapter 11 (Quality Improvement) stresses how important W. Edwards Deming's ideas are in understanding variation and how they apply to everyday life. TABLE OF CONTENTS: Preface Prologue 1. Probability 1.1 Basic Concepts 1.2 Properties of Probability 1.3 Methods of Enumeration 1.4 Conditional Probability 1.5 Independent Events 1.6 Bayes's Theorem 2. Discrete Distributions 2.1 Random Variables of the Discrete Type 2.2 Mathematical Expectation 2.3 The Mean, Variance, and Standard Deviation 2.4 Bernoulli Trials and the Binomial Distribution 2.5 The Moment-Generating Function 2.6 The Poisson Distribution 3. Continuous Distributions 3.1 Continuous-Type Data 3.2 Exploratory Data Analysis 3.3 Random Variables of the Continuous Type 3.4 The Uniform and Exponential Distributions 3.5 The Gamma and Chi-Square Distributions 3.6 The Normal Distribution 3.7 Additional Models 4. Bivariate Distributions 4.1 Distributions of Two Random Variables 4.2 The Correlation Coefficient 4.3 Conditional Distributions 4.4 The Bivariate Normal Distribution 5. Distributions of Functions of Random Variables 5.1 Functions of One Random Variable 5.2 Transformations of Two Random Variables 5.3 Several Independent Random Variables 5.4 The Moment-Generating Function Technique 5.5 Random Functions Associated with Normal Distributions 5.6 The Central Limit Theorem 5.7 Approximations for Discrete Distributions 6. Estimation 6.1 Point Estimation 6.2 Confidence Intervals for Means 6.3 Confidence Intervals for Difference of Two Means 6.4 Confidence Intervals for Variances 6.5 Confidence Intervals for Proportions 6.6 Sample Size. 6.7 A Simple Regression Problem 6.8 More Regression 7. Tests of Statistical Hypotheses 7.1 Tests about Proportions 7.2 Tests about One Mean 7.3 Tests of the Equality of Two Means 7.4 Tests for Variances 7.5 One-Factor Analysis of Variance 7.6 Two-Factor Analysis of Variance 7.7 Tests Concerning Regression and Correlation 8. Nonparametric Methods 8.1 Chi-Square Goodness of Fit Tests 8.2 Contingency Tables 8.3 Order Statistics 8.4 Distribution-Free Confidence Intervals for Percentiles 8.5 The Wilcoxon Tests 8.6 Run Test and Test for Randomness 8.7 Kolmogorov-Smirnov Goodness of Fit Test 8.8 Resampling Methods 9. Bayesian Methods 9.1 Subjective Probability 9.2 Bayesian Estimation 9.3 More Bayesian Concepts 10. Some Theory 10.1 Sufficient Statistics 10.2 Power of a Statistical Test 10.3 Best Critical Regions 10.4 Likelihood Ratio Tests 10.5 Chebyshev's Inequality and Convergence in Probability 10.6 Limiting Moment-Generating Functions 10.7 Asymptotic Distributions of Maximum Likelihood Estimators 11. Quality Improvement Through Statistical Methods 11.1 Time Sequences 11.2 Statistical Quality Control 11.3 General Factorial and 2k Factorial Designs 11.4 Understanding Variation A. Review of Selected Mathematical Techniques A.1 Algebra of Sets A.2 Mathematical Tools for the Hypergeometric Distribution A.3 Limits A.4 Infinite Series A.5 Integration A.6 Multivariate Calculus B. References C. Tables D. Answers to Odd-Numbered Exercises

Probability and Statistics for Engineers and Scientists: Pearson New International Edition

Author: Ronald E. Walpole,Raymond H. Myers,Sharon L. Myers,Keying E. Ye

Publisher: Pearson Higher Ed

ISBN: 1292037032

Category:

Page: 864

View: 3396

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For junior/senior undergraduates taking probability and statistics as applied to engineering, science, or computer science. This classic text provides a rigorous introduction to basic probability theory and statistical inference, with a unique balance between theory and methodology. Interesting, relevant applications use real data from actual studies, showing how the concepts and methods can be used to solve problems in the field. This revision focuses on improved clarity and deeper understanding. This latest edition is also available in as an enhanced Pearson eText. This exciting new version features an embedded version of StatCrunch, allowing students to analyze data sets while reading the book.

Probability and Statistical Inference

Author: Nitis Mukhopadhyay

Publisher: CRC Press

ISBN: 9780824703790

Category: Mathematics

Page: 665

View: 1898

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Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions develops notions of convergence in probability and distribution spotlights the central limit theorem (CLT) for the sample variance introduces sampling distributions and the Cornish-Fisher expansions concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity explains Basu's Theorem as well as location, scale, and location-scale families of distributions covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient summarizes Bayesian methods describes the monotone likelihood ratio (MLR) property handles variance stabilizing transformations provides a historical context for statistics and statistical discoveries showcases great statisticians through biographical notes Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.

John E. Freund's Mathematical Statistics with Applications: Pearson New International Edition

Author: Irwin Miller,Marylees Miller

Publisher: Pearson Higher Ed

ISBN: 1292037636

Category: Mathematics

Page: 480

View: 9438

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John E. Freund's Mathematical Statistics with Applications, Eighth Edition, provides a calculus-based introduction to the theory and application of statistics, based on comprehensive coverage that reflects the latest in statistical thinking, the teaching of statistics, and current practices. This text is appropriate for a two-semester or three-quarter calculus-based course in Introduction to Mathematical Statistics. It can also be used for a single-semester course emphasizing probability, probability distributions and densities, sampling, and classical statistical inference.

STATISTICAL INFERENCE : THEORY OF ESTIMATION

Author: MANOJ KUMAR SRIVASTAVA,ABDUL HAMID KHAN,NAMITA SRIVASTAVA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 812034930X

Category: Mathematics

Page: 808

View: 5693

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This book is sequel to a book Statistical Inference: Testing of Hypotheses (published by PHI Learning). Intended for the postgraduate students of statistics, it introduces the problem of estimation in the light of foundations laid down by Sir R.A. Fisher (1922) and follows both classical and Bayesian approaches to solve these problems. The book starts with discussing the growing levels of data summarization to reach maximal summarization and connects it with sufficient and minimal sufficient statistics. The book gives a complete account of theorems and results on uniformly minimum variance unbiased estimators (UMVUE)—including famous Rao and Blackwell theorem to suggest an improved estimator based on a sufficient statistic and Lehmann-Scheffe theorem to give an UMVUE. It discusses Cramer-Rao and Bhattacharyya variance lower bounds for regular models, by introducing Fishers information and Chapman, Robbins and Kiefer variance lower bounds for Pitman models. Besides, the book introduces different methods of estimation including famous method of maximum likelihood and discusses large sample properties such as consistency, consistent asymptotic normality (CAN) and best asymptotic normality (BAN) of different estimators. Separate chapters are devoted for finding Pitman estimator, among equivariant estimators, for location and scale models, by exploiting symmetry structure, present in the model, and Bayes, Empirical Bayes, Hierarchical Bayes estimators in different statistical models. Systematic exposition of the theory and results in different statistical situations and models, is one of the several attractions of the presentation. Each chapter is concluded with several solved examples, in a number of statistical models, augmented with exposition of theorems and results. KEY FEATURES • Provides clarifications for a number of steps in the proof of theorems and related results., • Includes numerous solved examples to improve analytical insight on the subject by illustrating the application of theorems and results. • Incorporates Chapter-end exercises to review student’s comprehension of the subject. • Discusses detailed theory on data summarization, unbiased estimation with large sample properties, Bayes and Minimax estimation, separately, in different chapters.

Trends and Perspectives in Linear Statistical Inference

LinStat, Istanbul, August 2016

Author: Müjgan Tez,Dietrich von Rosen

Publisher: Springer

ISBN: 3319732412

Category: Mathematics

Page: 257

View: 5520

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This volume features selected contributions on a variety of topics related to linear statistical inference. The peer-reviewed papers from the International Conference on Trends and Perspectives in Linear Statistical Inference (LinStat 2016) held in Istanbul, Turkey, 22-25 August 2016, cover topics in both theoretical and applied statistics, such as linear models, high-dimensional statistics, computational statistics, the design of experiments, and multivariate analysis. The book is intended for statisticians, Ph.D. students, and professionals who are interested in statistical inference.

Fundamentals of Queueing Theory

Author: John F. Shortle,James M. Thompson,Donald Gross,Carl M. Harris

Publisher: John Wiley & Sons

ISBN: 111894352X

Category: Business & Economics

Page: 576

View: 6280

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The definitive guide to queueing theory and its practical applications—features numerous real-world examples of scientific, engineering, and business applications Thoroughly updated and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fifth Edition presents the statistical principles and processes involved in the analysis of the probabilistic nature of queues. Rather than focus narrowly on a particular application area, the authors illustrate the theory in practice across a range of fields, from computer science and various engineering disciplines to business and operations research. Critically, the text also provides a numerical approach to understanding and making estimations with queueing theory and provides comprehensive coverage of both simple and advanced queueing models. As with all preceding editions, this latest update of the classic text features a unique blend of the theoretical and timely real-world applications. The introductory section has been reorganized with expanded coverage of qualitative/non-mathematical approaches to queueing theory, including a high-level description of queues in everyday life. New sections on non-stationary fluid queues, fairness in queueing, and Little’s Law have been added, as has expanded coverage of stochastic processes, including the Poisson process and Markov chains. • Each chapter provides a self-contained presentation of key concepts and formulas, to allow readers to focus independently on topics relevant to their interests • A summary table at the end of the book outlines the queues that have been discussed and the types of results that have been obtained for each queue • Examples from a range of disciplines highlight practical issues often encountered when applying the theory to real-world problems • A companion website features QtsPlus, an Excel-based software platform that provides computer-based solutions for most queueing models presented in the book. Featuring chapter-end exercises and problems—all of which have been classroom-tested and refined by the authors in advanced undergraduate and graduate-level courses—Fundamentals of Queueing Theory, Fifth Edition is an ideal textbook for courses in applied mathematics, queueing theory, probability and statistics, and stochastic processes. This book is also a valuable reference for practitioners in applied mathematics, operations research, engineering, and industrial engineering.

Statistics: Pearson New International Edition

Author: James T. McClave,Terry Sincich

Publisher: Pearson Higher Ed

ISBN: 1292035854

Category: Mathematics

Page: 816

View: 4108

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Classic, yet contemporary. Theoretical, yet applied. McClave & Sincich’s Statistics gives you the best of both worlds. This text offers a trusted, comprehensive introduction to statistics that emphasizes inference and integrates real data throughout. The authors stress the development of statistical thinking, the assessment of credibility, and value of the inferences made from data. The Twelfth Edition infuses a new focus on ethics, which is critically important when working with statistical data. Chapter Summaries have a new, study-oriented design, helping students stay focused when preparing for exams. Data, exercises, technology support, and Statistics in Action cases are updated throughout the book. In addition, MyStatLab will have increased exercise coverage and two new banks of questions to draw from: Getting Ready for Stats and Conceptual Question Library. Ideal for one- or two-semester courses in introductory statistics, this text assumes a mathematical background of basic algebra. Flexibility is built in for instructors who teach a more advanced course, with optional footnotes about calculus and the underlying theory.

First Course in Statistics, A: Pearson New International Edition

Author: James T McClave,Terry Sincich

Publisher: Pearson Higher Ed

ISBN: 1292036818

Category: Mathematics

Page: 600

View: 2614

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Classic, yet contemporary. Theoretical, yet applied. McClave & Sincich’s Statistics: A First Course in Statistics gives you the best of both worlds. This text offers a trusted, comprehensive introduction to statistics that emphasizes inference and integrates real data throughout. The authors stress the development of statistical thinking, the assessment of credibility, and value of the inferences made from data. The Eleventh Edition infuses a new focus on ethics, which is critically important when working with statistical data. Chapter Summaries have a new, study-oriented design, helping students stay focused when preparing for exams. Data, exercises, technology support, and Statistics in Action cases are updated throughout the book. In addition, MyStatLab will have increased exercise coverage and two new banks of questions to draw from: Getting Ready for Stats and Conceptual Question Library. Ideal for one- or two-semester courses in introductory statistics, this text assumes a mathematical background of basic algebra. Flexibility is built in for instructors who teach a more advanced course, with optional footnotes about calculus and the underlying theory.

Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science

Volume III Foundations and Philosophy of Statistical Theories in the Physical Sciences

Author: W.L. Harper,C.A. Hooker

Publisher: Springer Science & Business Media

ISBN: 9401014388

Category: Science

Page: 244

View: 6473

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In May of 1973 we organized an international research colloquium on foundations of probability, statistics, and statistical theories of science at the University of Western Ontario. During the past four decades there have been striking formal advances in our understanding of logic, semantics and algebraic structure in probabilistic and statistical theories. These advances, which include the development of the relations between semantics and metamathematics, between logics and algebras and the algebraic-geometrical foundations of statistical theories (especially in the sciences), have led to striking new insights into the formal and conceptual structure of probability and statistical theory and their scientific applications in the form of scientific theory. The foundations of statistics are in a state of profound conflict. Fisher's objections to some aspects of Neyman-Pearson statistics have long been well known. More recently the emergence of Bayesian statistics as a radical alternative to standard views has made the conflict especially acute. In recent years the response of many practising statisticians to the conflict has been an eclectic approach to statistical inference. Many good statisticians have developed a kind of wisdom which enables them to know which problems are most appropriately handled by each of the methods available. The search for principles which would explain why each of the methods works where it does and fails where it does offers a fruitful approach to the controversy over foundations.