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Mathematical statistics and data analysis

Author: John A Rice
Publisher: Belmont, CA : Thomson/Brooks/Cole, ©2007.
Series: Duxbury advanced series.
Edition/Format:   Book : English : 3rd edView all editions and formats
Database:WorldCat
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Document Type: Book
All Authors / Contributors: John A Rice
ISBN: 0534399428 9780534399429 0495110892 9780495110897
OCLC Number: 71364578
Notes: System requirements for computer disk: IBM-compatible PC; DOS. Files in ASCII and Minitab formats.
Description: 1 v. (various pagings) : ill. ; 25 cm. + 1 CD-ROM (4 3/4 in.)
Contents: 1 Probability 1 --
1.2 Sample Spaces 2 --
1.3 Probability Measures 4 --
1.4 Computing Probabilities: Counting Methods 6 --
1.4.1 The Multiplication Principle 7 --
1.4.2 Permutations and Combinations 9 --
1.5 Conditional Probability 16 --
1.6 Independence 23 --
2 Random Variables 35 --
2.1 Discrete Random Variables 35 --
2.1.1 Bernoulli Random Variables 37 --
2.1.2 The Binomial Distribution 38 --
2.1.3 The Geometric and Negative Binomial Distributions 40 --
2.1.4 The Hypergeometric Distribution 42 --
2.1.5 The Poisson Distribution 42 --
2.2 Continuous Random Variables 47 --
2.2.1 The Exponential Density 50 --
2.2.2 The Gamma Density 53 --
2.2.3 The Normal Distribution 54 --
2.2.4 The Beta Density 58 --
2.3 Functions of a Random Variable 58 --
3 Joint Distributions 71 --
3.2 Discrete Random Variables 72 --
3.3 Continuous Random Variables 75 --
3.4 Independent Random Variables 84 --
3.5 Conditional Distributions 87 --
3.5.1 The Discrete Case 87 --
3.5.2 The Continuous Case 88 --
3.6 Functions of Jointly Distributed Random Variables 96 --
3.6.1 Sums and Quotients 96 --
3.6.2 The General Case 99 --
3.7 Extrema and Order Statistics 104 --
4 Expected Values 116 --
4.1 The Expected Value of a Random Variable 116 --
4.1.1 Expectations of Functions of Random Variables 121 --
4.1.2 Expectations of Linear Combinations of Random Variables 124 --
4.2 Variance and Standard Deviation 130 --
4.2.1 A Model for Measurement Error 135 --
4.3 Covariance and Correlation 138 --
4.4 Conditional Expectation and Prediction 147 --
4.4.2 Prediction 152 --
4.5 The Moment-Generating Function 155 --
4.6 Approximate Methods 161 --
5 Limit Theorems 177 --
5.2 The Law of Large Numbers 177 --
5.3 Convergence in Distribution and the Central Limit Theorem 181 --
6 Distributions Derived from the Normal Distribution 192 --
6.2 x[superscript 2], t, and F Distributions 192 --
6.3 The Sample Mean and the Sample Variance 195 --
7 Survey Sampling 199 --
7.2 Population Parameters 200 --
7.3 Simple Random Sampling 202 --
7.3.1 The Expectation and Variance of the Sample Mean 203 --
7.3.2 Estimation of the Population Variance 210 --
7.3.3 The Normal Approximation to the Sampling Distribution of X 214 --
7.4 Estimation of a Ratio 220 --
7.5 Stratified Random Sampling 227 --
7.5.1 Introduction and Notation 227 --
7.5.2 Properties of Stratified Estimates 228 --
7.5.3 Methods of Allocation 232 --
8 Estimation of Parameters and Fitting of Probability Distributions 255 --
8.2 Fitting the Poisson Distribution to Emissions of Alpha Particles 255 --
8.3 Parameter Estimation 257 --
8.4 The Method of Moments 260 --
8.5 The Method of Maximum Likelihood 267 --
8.5.1 Maximum Likelihood Estimates of Multinomial Cell Probabilities 272 --
8.5.2 Large Sample Theory for Maximum Likelihood Estimates 274 --
8.5.3 Confidence Intervals from Maximum Likelihood Estimates 279 --
8.6 The Bayesian Approach to Parameter Estimation 285 --
8.6.1 Further Remarks on Priors 294 --
8.6.2 Large Sample Normal Approximation to the Posterior 296 --
8.6.3 Computational Aspects 297 --
8.7 Efficiency and the Cramer-Rao Lower Bound 298 --
8.7.1 An Example: The Negative Binomial Distribution 302 --
8.8 Sufficiency 305 --
8.8.1 A Factorization Theorem 306 --
8.8.2 The Rao-Blackwell Theorem 310 --
9 Testing Hypotheses and Assessing Goodness of Fit 329 --
9.2 The Neyman-Pearson Paradigm 331 --
9.2.1 Specification of the Significance Level and the Concept of a p-value 334 --
9.2.2 The Null Hypothesis 335 --
9.2.3 Uniformly Most Powerful Tests 336 --
9.3 The Duality of Confidence Intervals and Hypothesis Tests 337 --
9.4 Generalized Likelihood Ratio Tests 339 --
9.5 Likelihood Ratio Tests for the Multinomial Distribution 341 --
9.6 The Poisson Dispersion Test 347 --
9.7 Hanging Rootograms 349 --
9.8 Probability Plots 352 --
9.9 Tests for Normality 358 --
10 Summarizing Data 377 --
10.2 Methods Based on the Cumulative Distribution Function 378 --
10.2.1 The Empirical Cumulative Distribution Function 378 --
10.2.2 The Survival Function 380 --
10.2.3 Quantile-Quantile Plots 385 --
10.3 Histograms, Density Curves, and Stem-and-Leaf Plots 389 --
10.4 Measures of Location 392 --
10.4.1 The Arithmetic Mean 393 --
10.4.2 The Median 395 --
10.4.3 The Trimmed Mean 397 --
10.4.4 M Estimates 397 --
10.4.5 Comparison of Location Estimates 398 --
10.4.6 Estimating Variability of Location Estimates by the Bootstrap 399 --
10.5 Measures of Dispersion 401 --
10.6 Boxplots 402 --
10.7 Exploring Relationships with Scatterplots 404 --
11 Comparing Two Samples 420 --
11.2 Comparing Two Independent Samples 421 --
11.2.1 Methods Based on the Normal Distribution 421 --
11.2.2 Power 433 --
11.2.3 A Nonparametric Method-The Mann-Whitney Test 435 --
11.2.4 Bayesian Approach 443 --
11.3 Comparing Paired Samples 444 --
11.3.1 Methods Based on the Normal Distribution 446 --
11.3.2 A Nonparametric Method-The Signed Rank Test 448 --
11.3.3 An Example-Measuring Mercury Levels in Fish 450 --
11.4 Experimental Design 452 --
11.4.1 Mammary Artery Ligation 452 --
11.4.2 The Placebo Effect 453 --
11.4.3 The Lanarkshire Milk Experiment 453 --
11.4.4 The Portacaval Shunt 454 --
11.4.5 FD&C Red No. 40 455 --
11.4.6 Further Remarks on Randomization 456 --
11.4.7 Observational Studies, Confounding, and Bias in Graduate Admissions 457 --
11.4.8 Fishing Expeditions 458 --
12 The Analysis of Variance 477 --
12.2 The One-Way Layout 477 --
12.2.1 Normal Theory; the F Test 478 --
12.2.2 The Problem of Multiple Comparisons 485 --
12.2.3 A Nonparametric Method-The Kruskal-Wallis Test 488 --
12.3 The Two-Way Layout 489 --
12.3.1 Additive Parametrization 489 --
12.3.2 Normal Theory for the Two-Way Layout 492 --
12.3.3 Randomized Block Designs 500 --
12.3.4 A Nonparametric Method-Friedman's Test 503 --
13 The Analysis of Categorical Data 514 --
13.2 Fisher's Exact Test 514 --
13.3 The Chi-Square Test of Homogeneity 516 --
13.4 The Chi-Square Test of Independence 520 --
13.5 Matched-Pairs Designs 523 --
13.6 Odds Ratios 526 --
14 Linear Least Squares 542 --
14.2 Simple Linear Regression 547 --
14.2.1 Statistical Properties of the Estimated Slope and Intercept 547 --
14.2.2 Assessing the Fit 550 --
14.2.3 Correlation and Regression 560 --
14.3 The Matrix Approach to Linear Least Squares 564 --
14.4 Statistical Properties of Least Squares Estimates 567 --
14.4.1 Vector-Valued Random Variables 567 --
14.4.2 Mean and Covariance of Least Squares Estimates 573 --
14.4.3 Estimation of [gamma superscript 2] 575 --
14.4.4 Residuals and Standardized Residuals 576 --
14.4.5 Inference about [beta] 577 --
14.5 Multiple Linear Regression-An Example 580 --
14.6 Conditional Inference, Unconditional Inference, and the Bootstrap 585 --
14.7 Local Linear Smoothing 587 --
Appendix A Common Distributions A1.
Series Title: Duxbury advanced series.
Responsibility: John A. Rice.

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