No Place For Devils (Diablos Locos Motorcycle Club Book 1)

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations. Cover Preface to the Second Edition Preface to the First Edition Contents List of Tables List of Figures List of Examples Chapter 1: Probability Theory 1.1 Set Theory 1.2 Basics of Probability Theory 1.3 Conditional Probability and Independence 1.4 Random Variables 1.5 Distribution Functions 1.6 Density and Mass Functions 1.7 Exercises 1.8 Miscellanea Chapter 2: Transformations and Expectations 2.1 Distributions of Functions of a Random Variable 2.2 Expected Values 2.3 Moments and Moment Generating Functions 2.4 Differentiating under an Integral Sign 2.5 Exercises 2.6 Miscellanea Chapter 3: Common Families of Distributions 3.1 Introduction 3.2 Discrete Distributions 3.3 Continuous Distributions 3.4 Exponential Families 3.5 Location and Scale Families 3.6 Inequalities and Identities 3.7 Exercises 3.8 Miscellanea Chapter 4: Multiple Random Variables 4.1 Joint and Marginal Distributions 4.2 Conditional Distributions and Independence 4.3 Bivariate Transformations 4.4 Hierarchical Models and Mixture Distributions 4.5 Covariance and Correlation 4.6 Multivariate Distributions 4.7 Inequalities 4.8 Exercises 4.9 Miscellanea Chapter 5: Properties of a Random Sample 5.1 Basic Concepts of Random Samples 5.2 Sums of Random Variables from a Random Sample 5.3 Sampling from the Normal Distribution 5.4 Order Statistics 5.5 Convergence Concepts 5.6 Generating a Random Sample 5.7 Exercises 5.8 Miscellanea Chapter 6: Principles of Data Reduction 6.1 Introduction 6.2 The Sufficiency Principle 6.3 The Likelihood Principle 6.4 The Equivariance Principle 6.5 Exercises 6.6 Miscellanea Chapter 7: Point Estimation 7.1 Introduction 7.2 Methods of Finding Estimators 7.3 Methods of Evaluating Estimators 7.4 Exercises 7.5 Miscellanea Chapter 8: Hypothesis Testing 8.1 Introduction 8.2 Methods of Finding Tests 8.3 Methods of Evaluating Tests 8.4 Exercises 8.5 Miscellanea Chapter 9: Interval Estimation 9.1 Introduction 9.2 Methods of Finding Interval Estimators 9.3 Methods of Evaluating Interval Estimators 9.4 Exercises 9.5 Miscellanea Chapter 10: Asymptotic Evaluations 10.1 Point Estimation 10.2 Robustness 10.3 Hypothesis Testing 10.4 Interval Estimation 10.5 Exercises 10.6 Miscellanea Chapter 11: Analysis of Variance and Regression 11.1 Introduction 11.2 Oneway Analysis of Variance 11.3 Simple Linear Regression 11.4 Exercises 11.5 Miscellanea Chapter 12: Regression Models 12.1 Introduction 12.2 Regression with Errors in Variables 12.3 Logistic Regression 12.4 Robust Regression 12.5 Exercises 12.6 Miscellanea Appendix: Computer Algebra Table of Common Distributions References Author Index Subject Index George Casella and Roger L. Berger's new edition builds the theoretical statistics from the first principals of probability theory. Thoroughly and completely, the authors start with the basics of probability and then move on to develop the theory of statistical inference using techniques, definitions, and statistical concepts.-- Restructures some material to provide better ordering of topics in Chapters 3-11.-- Provides updated and expanded Exercises and Miscellanea in all chapters.-- Includes strong coverage of topics such as ancillary, invariance, Bayesian methods, pivots, Stein estimation, and errors in variables and inequalities.-- Includes a thorough introduction to decision theory that features the most modern material available.-- Separates the finding of appropriate statistical techniques and the methods of evaluating these techniques. This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. This book can be used for readers who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations. Probability Theory -- Transformations And Expectations -- Common Families Of Distributions -- Multiple Random Variables -- Properties Of A Random Sample -- Principles Of Data Reduction -- Point Estimation -- Hypothesis Testing -- Interval Estimation -- Asymptotic Evaluations -- Analysis Of Variance And Regression -- Regression Models. George Casella, Roger L. Berger. Includes Bibliographical References (p. [629]-644) And Indexes. The subject of probability theory is the foundation upon which all of statistics is built, providing a means for modeling populations, experiments, or almost anything else that could be considered a random phenomenon.