Statistics, A Concise Mathematical Introduction for Students, Scientists, and Engineers by David W. Scott -- Read -- Imperial Library of Trantor

Index

Cover Table of Contents Preface 1 Data Analysis and Understanding

1.1 Exploring the Distribution of Data 1.2 Exploring Prediction Using Data Problems

2 Classical Probability

2.1 Experiments with Equally Likely Outcomes 2.2 Probability Laws 2.3 Counting Methods 2.4 Countable Sets: Implications as 2.5 Kolmogorov's Axioms 2.6 Reliability: Series Versus Parallel Networks Problems

3 Random Variables and Models Derived From Classical Probability and Postulates

4 Bivariate Random Variables, Transformations, and Simulations

4.1 Bivariate Continuous Random Variables 4.2 Change of Variables 4.3 Simulations Problems

5 Approximations and Asymptotics

5.1 Why Do We Like Random Samples? 5.2 Useful Inequalities 5.3 Sequences of Random Variables 5.4 Central Limit Theorem 5.5 Delta Method and Variance‐stabilizing Transformations Problems Notes

6 Parameter Estimation

6.1 Desirable Properties of an Estimator 6.2 Moments of the Sample Mean and Variance 6.3 Method of Moments (MoM) 6.4 Sufficient Statistics and Data Compression 6.5 Bayesian Parameter Estimation 6.6 Maximum Likelihood Parameter Estimation 6.7 Information Inequalities and the Cramér–Rao Lower Bound Problems

7 Hypothesis Testing

7.1 Setting up a Hypothesis Test 7.2 Best Critical Region for Simple Hypotheses 7.3 Best Critical Region for a Composite Alternative Hypothesis 7.4 Reporting Results: ‐values and Power 7.5 Multiple Testing and the Bonferroni Correction Problems

8 Confidence Intervals and Other Hypothesis Tests

8.1 Confidence Intervals 8.2 Hypotheses About the Variance and the ‐Distribution 8.3 Pearson's Chi‐Squared Tests 8.4 Correlation Coefficient Tests and CIs 8.5 Linear Regression 8.6 Analysis of Variance Problems

9 Topics in Statistics

9.1 MSE and Histogram Bin Width Selection 9.2 An Optimal Stopping Time Problem 9.3 Compound Random Variables 9.4 Simulation and the Bootstrap 9.5 Multiple Linear Regression 9.6 Experimental Design 9.7 Logistic Regression, Poisson Regression, and the Generalized Linear Model 9.8 Robustness 9.9 Conclusions

Appendices

A Notation Used in This Book B Common Distributions C Using R and Mathematica For This Text

Bibliography Index End User License Agreement