Читать книгу Statistics - David W. Scott - Страница 2
ОглавлениеTable of Contents
1 Cover
2 Preface
3 1 Data Analysis and Understanding 1.1 Exploring the Distribution of Data 1.2 Exploring Prediction Using Data Problems
4 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
5 3 Random Variables and Models Derived From Classical Probability and Postulates 3.1 Random Variables and Probability Distributions: Discrete Uniform Example 3.2 The Univariate Probability Density Function: Continuous Uniform Example 3.3 Summary Statistics: Central and Non‐Central Moments 3.4 Binomial Experiments 3.5 Waiting Time for a Success: Geometric PMF 3.6 Waiting Time for Successes: Negative Binomial 3.7 Poisson Process and Distribution 3.8 Waiting Time for Poisson Events: Negative Exponential PDF 3.9 The Normal Distribution (Also Known as the Gaussian Distribution) Problems
6 4 Bivariate Random Variables, Transformations, and Simulations 4.1 Bivariate Continuous Random Variables 4.2 Change of Variables 4.3 Simulations Problems
7 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
8 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
9 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
10 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
11 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
12 Appendices A Notation Used in This Book B Common Distributions C Using R and Mathematica For This Text
13 Bibliography
14 Index
List of Tables
1 Chapter 1Table 1.1 Lord Rayleigh's 24 measurements (sorted) of the weight of a sample ...
2 Chapter 3Table 3.1 Probabilities for roll of a single die.Table 3.2 The 36 equally likely simple outcomes when rolling a pair of dice.Table 3.3 Probability distribution function for the sum of pips on two dice.
3 Chapter 7Table 7.1 Truth table for hypothesis testing.Table 7.2 Upper critical values for the two‐sided ‐test versus ‐test.
4 Chapter 8Table 8.1 Data for testing the adequacy of a normal model.Table 8.2 Contingency table for Scottish children.Table 8.3 Expected values assuming independence of sex and hair color.
List of Illustrations
1 Chapter 1Figure 1.1 Displays of the father–son height data collected by Karl Pearson:...Figure 1.2 Histograms of the sons' heights (top row) and fathers' heights (b...Figure 1.3 Displays of Lord Rayleigh's 24 measurements of the atomic weight ...Figure 1.4 Scatter diagrams of the raw and ‐transformed body and brain weig...Figure 1.5 Analysis of the number of O‐ring failures for the first 24 Space ...Figure 1.6 Father–son height data collected by Karl Pearson.Figure 1.7 Box–Cox transformation on natural and log scales.
2 Chapter 2Figure 2.1 (Left) Venn diagram of the classical probability experiment rolli...Figure 2.2 Four possible relationships between events and .Figure 2.3 Probability that students all have different birthdays, plotted...Figure 2.4 (Left) Venn diagram of partition of into sets ; (middle) set...Figure 2.5 Illustration of the FPC. Select one of , then one of , and fina...Figure 2.6 A series network (left) and parallel network (right) of compone...
3 Chapter 3Figure 3.1 (Left) The cumulative distribution function for the roll of a sin...Figure 3.2 (Left) The cumulative distribution function for the sum of pips o...Figure 3.3 (Left) The CDF for a density; and (right) its PDF.Figure 3.4 The shaded areas give the probabilities of the events , , and Figure 3.5 The CDF and PDF of an isosceles triangular distribution.Figure 3.6 Binomial PMF for various combinations of and .Figure 3.7 Binomial CDF for and as in Figure 3.6.Figure 3.8 The two disjoint events that result in calls in , ignoring the...Figure 3.9 Examples of the Poisson PMF, where .Figure 3.10 Examples of the discrete Poisson PMF, Pois , and the continuous ...Figure 3.11 Gauss on the German Mark bill. Note the Gaussian curve.Figure 3.12 Standard normal CDF, , and PDF, , for .
4 Chapter 4Figure 4.1 Joint bivariate PMF. Each arrow displays a probability of .Figure 4.2 Conditional PDF, , before normalization.Figure 4.3 Transformations of a r.v.; see text.Figure 4.4 Sample transformations: and . The range and domain of this tra...Figure 4.5 Standard Cauchy and normal PDFs.Figure 4.6 Generic PIT diagram. The red strip represents the event while t...
5 Chapter 5Figure 5.1 Example of a convex function with two red tangent line segments...
6 Chapter 6Figure 6.1 Nine examples of possible normal fits to a random sample of 50 po...Figure 6.2 From left to right: a histogram of the 41 data points; the Beta ...
7 Chapter 7Figure 7.1 (Left) For two roof construction techniques, hypothetical PDFs ...Figure 7.2 Critical regions based upon for testing two shifted normal PDFs...Figure 7.3 (Left) The log‐likelihood ratio for a sample of negative expone...Figure 7.4 Alternative 95% confidence level tests for our example. (Left) ...Figure 7.5 (Left) Topo map; (right) earthquake epicenters.Figure 7.6 Histograms of times between eruptions (in days) for all 247 erupt...Figure 7.7 Fits to Lord Rayleigh's data under the null and alternative hypot...Figure 7.8 (Left) Power function with . The critical region is shown in gra...Figure 7.9 Draft lottery numbers 1–366 by month. The monthly average is the ...
8 Chapter 8Figure 8.1 (Left frames) A simulation study showing 100 95% confidence inter...Figure 8.2 (Left) Examples of the PDF for . (Right) Examples of the PDF...Figure 8.3 Critical values for as the sample size increases.Figure 8.4 Ten thousand simulations of the ‐statistic (8.46) with , , and...
9 Chapter 9Figure 9.1 For a frequency histogram, the notation used to denote the locati...Figure 9.2 For several sample sizes and the density, the histogram curve...Figure 9.3 Comparison of the number of bins recommended by the Sturges (), ...Figure 9.4 Three histograms of a Beta sample with .Figure 9.5 (Left) Optimal stopping point as a function of the population s...Figure 9.6 Simulation and bootstrap analysis of the sample mean and sample m...Figure 9.7 Surface of predicted average mold strength as a function of the t...Figure 9.8 (Left) Poisson and (right) logistic regression models fitted by t...Figure 9.9 (a) points satisfying with one outlier at ; (b) with 40 ra...Figure 9.10 (a) MLE and (b) normal fits to a random sample of 400 points...
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