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EB

EB

ONLINE

Second edition

London : Academic Press, imprint of Elsevier, 2015

1 online zdroj

ISBN 9780124171329 (e-kniha)

ISBN 9780124171138 (print)

Obsahuje bibliografické odkazy a rejstřík.

Descriptive statistics -- Basic concepts from probability theory -- Additional topics in probability -- Sampling distributions -- Statistical estimation -- Hypothesis testing -- Goodness-of-fit tests and applications -- Linear regression models -- Design of experiments -- Analysis of variance -- Bayesian estimation and inference -- Nonparametric tests -- Empirical methods -- Some issues in statistical applications: an overview.

Mathematical Statistics with Applications, Second Edition, gives an up-to-date introduction to the theory of statistics with a wealth of real-world applications that will help students approach statistical problem solving in a logical manner. The book introduces many modern statistical computational and simulation concepts that are not covered in other texts; such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. Goodness of fit methods are included to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Engineering students, especially, will find these methods to be very important in their studies..

Print version record.

001483085

Preface to Second Edition xv // Acknowledgments xix // About the Authors xxi // Flow Chart xxiii // CHAPTER 1 Descriptive Statistics 1 // 1.1 Introduction 2 // 1.1.1 Data Collection 3 // 1.2 Basic Concepts 4 // 1.2.1 Types of Data 5 // 1.3 Sampling Schemes 8 // 1.3.1 Errors in Sample Data 12 // 1.3.2 Sample Size 12 // 1.4 Graphical Representation of Data 13 // 1.5 Numerical Description of Data 26 // 1.5.1 Numerical Measures for Grouped Data 30 // 1.5.2 Box Plots 33 // 1.6 Computers and Statistics 39 // 1.7 Chapter Summary 39 // 1.8 Computer Examples 41 // 1.8.1 R Introduction and Examples 41 // 1.8.2 Minitab Examples 44 // 1.8.3 SPSS Examples 46 // 1.8.4 SAS Examples 48 // Projects for Chapter 1 51 // CHAPTER 2 Basic Concepts from Probability Theory 53 // 2.1 Introduction 54 // 2.2 Random Events and Probability 55 // 2.3 Counting Techniques and Calculation of Probabilities 63 // 2.4 The Conditional Probability, Independence, and Bayes’ Rule.70 // 2.5 Random Variables and Probability Distributions 82 // 2.6 Moments and Moment-Generating Functions 91 // 2.6.1 Skewness and Kurtosis 96 // 2.7 Chapter Summary 104 // 2.8 Computer Examples (Optional) 105 // 2.8.1 Examples Using R 105 // 2.8.2 Minitab Computations 106 // 2.8.2 SPSS Examples 107 // 2.8.3 SAS Examples 107 // Projects for Chapter 2 108 // CHAPTER 3 Additional Topics in Probability 111 // 3.1 Introduction 112 // 3.2 Special Distribution Functions 112 // 3.2.1 The Binomial Probability Distribution 113 // 3.2.2 Poisson Probability Distribution 117 // 3.2.3 Uniform Probability Distribution 120 // 3.2.4 Normal Probability Distribution 122 // 3.2.5 Gamma Probability Distribution 129 // 3.3 Joint Probability Distributions 139 // 3.3.1 Covariance and Correlation 147 // 3.4 Functions of Random Variables 152 // 3.4.1 Method of Distribution Functions 152 //

3.4.2 The pdf of Y=g(X), Where g is Differentiable and Monotone Increasing or Decreasing 154 // 3.4.3 Probability Integral Transformation 154 // 3.4.4 Functions of Several Random Variables: Method of Distribution Functions 155 // 3.4.5 Transformation Method 155 // 3.5 Limit Theorems 159 // 3.6 Chapter Summary 168 // 3.7 Computer Examples (Optional) 170 // 3.7.1 The R-Examples 170 // 3.7.2 Minitab Examples 171 // 3.7.2 SPSS Examples 173 // 3.7.3 SAS Examples 173 // Projects for Chapter 3 175 // CHAPTER 4 Sampling Distributions 177 // 4.1 Introduction 178 // 4.1.1 Finite Population 181 // 4.2 Sampling Distributions Associated with Normal Populations.. 184 // 4.2.1 Chi-Square Distribution 186 // 4.2.2 Student/-Distribution 191 // 4.2.3 F-Distribution 195 // 4.3 Order Statistics 200 // 4.4 Large Sample Approximations 205 // 4.4.1 The Normal Approximation to the Binomial // Distribution 206 // 4.5 Chapter Summary 210 // 4.6 Computer Examples 211 // 4.6.1 Examples Using R 211 // 4.6.2 Minitab Examples 213 // 4.6.3 SPSS Examples 214 // 4.6.4 SAS Examples 214 // Projects for Chapter 4 215 // CHAPTER 5 Statistical Estimation 219 // 5.1 Introduction 220 // 5.2 The Methods of Finding Point Estimators 221 // 5.2.1 The Method of Moments 222 // 5.2.2 The Method of Maximum Likelihood 227 // Some Additional Probability Distributions 234 // 5.3 Some Desirable Properties of Point Estimators 245 // 5.3.1 Unbiased Estimators 245 // 5.3.2 Sufficiency 250 // 5.4 A Method of Finding the Confidence Interval: // Pivotal Method 261 // 5.5 One Sample Confidence Intervals 269 // 5.5.1 Large Sample Confidence Intervals 269 // 5.5.2 Confidence Interval for Proportion, p 272 // 5.5.3 Small Sample Confidence Intervals for ? 275 // 5.6 A Confidence Interval for the Population Variance 284 // 5.7 Confidence Interval Concerning Two Population Parameters 289 // 5.8 Chapter Summary 298 //

5.9 Computer Examples 299 // 5.9.1 Examples Using R 299 // 5.9.2 Minitab Examples 301 // 5.9.3 SPSS Examples 302 // 5.9.4 SAS Examples 303 // Projects for Chapter 5 303 // CHAPTER 6 Hypothesis Testing 311 // 6.1 Introduction 312 // 6.1.1 Sample Size 320 // 6.2 The Neyman-Pearson Lemma 323 // 6.3 Likelihood Ratio Tests 328 // 6.4 Hypotheses for a Single Parameter 333 // 6.4.1 The p-Value 333 // 6.4.2 Hypothesis Testing for a Single Parameter 336 // 6.5 Testing of Hypotheses for Two Samples 345 // 6.5.1 Independent Samples 345 // 6.5.2 Dependent Samples 353 // 6.6 Chapter Summary 359 // 6.7 Computer Examples 360 // 6.7.1 R-Examples 360 // 6.7.2 Minitab Examples 363 // 6.7.3 SPSS Examples 365 // 6.7.4 SAS Examples 366 // Projects for Chapter 6 368 // CHAPTER 7 Goodness-of-Fit Tests Applications 371 // 7.1 Introduction 372 // 7.2 The Chi-Square Tests for Count Data 372 // 7.2.1 Testing the Parameters of a Multinomial Distribution: Goodness-of-Fit Test 374 // 7.2.2 Contingency Table: Test for Independence 376 // 7.3 Goodness-of-Fit Tests to Identify the Probability Distribution 381 // 7.3.1 Pearson’s Chi-Square Test 381 // 7.3.2 The Kolmogorov-Smimov Test: (One Population) 384 // 7.3.3 The Anderson-Darling Test 387 // 7.3.4 Shapiro-Wilk Normality Test 388 // 7.3.5 The P-P Plots and Q-Q Plots 389 // 7.4 Applications: Parametric Analysis 392 // 7.4.1 Global Warming 392 // 7.4.2 Hurricane Katrina 393 // 7.4.3 National Unemployment 396 // 7.4.4 Brain Cancer 397 // 7.4.5 Rainfall 399 // 7.4.6 Prostate Cancer 402 // 7.6 Chapter Summary 406 // 7.7 Computer Examples 406 // 7.7.1 R-Commands 406 // 7.7.2 Minitab Examples 407 // Projects for Chapter 7 408 // CHAPTER 8 Linear Regression Models 409 // 8.1 Introduction 410 // 8.2 The Simple Linear Regression Model 411 // 8.2.1 The Method of Least-Squares 413 // 8.2.2 Derivation of /?0 and ßt 414 //

8.2.3 Quality of the Regression 418 // 8.2.4 Properties of the Least-Squares Estimators for the Model Y=ßo+ßiX+e 420 // 8.2.5 Estimation of Error Variance a2 422 // 8.3 Inferences on the Least-Squares Estimators 425 // 8.3.1 Analysis of Variance (ANOVA) Approach to Regression 430 // 8.4 Predicting a Particular Value of Y 433 // 8.5 Correlation Analysis 436 // 8.6 Matrix Notation for Linear Regression 440 // 8.6.1 ANOVA for Multiple Regression 444 // 8.7 Regression Diagnostics 446 // 8.8 Chapter Summary 449 // 8.9 Computer Examples 450 // 8.9.1 Examples Using R 450 // 8.9.2 Minitab Examples 453 // 8.9.3 SPSS Examples 454 // 8.9.4 SAS Examples 454 // Project for Chapter 8 456 // CHAPTERS Design of Experiments 459 // 9.1 Introduction 460 // 9.2 Concepts from Experimental Design 461 // 9.2.1 Basic Terminology 461 // 9.2.2 Fundamental Principles: Replication, Randomization, and Blocking 466 // 9.2.3 Some Specific Designs 469 // 9.3 Factorial Design 477 // 9.3.1 One-Factor-at-a-Time Design 478 // 9.3.2 Full Factorial Design 480 // 9.3.3 Fractional Factorial Design 480 // 9.4 Optimal Design 481 // 9.4.1 Choice of Optimal Sample Size 482 // 9.5 The Taguchi Methods 484 // 9.6 Chapter Summary 488 // 9.7 Computer Examples 489 // 9.7.1 Examples Using R 489 // 9.7.2 Minitab Examples 491 // 9.7.3 SAS Examples 491 // Projects for Chapter 9 493 // CHAPTER 10 Analysis of Variance 495 // 10.1 Introduction 496 // 10.2 ANOVA Method for Two Treatments (Optional) 498 // 10.3 ANOVA for Completely Randomized Design 505 // 10.3.1 The p-Value Approach 510 // 10.3.2 Testing the Assumptions for One-Way ANOVA 512 // 10.3.3 Model for One-Way ANOVA (Optional) 517 // 10.4 Two-Way ANOVA. Randomized Complete Block Design 521 // 10.5 Multiple Comparisons 528 // 10.6 Chapter Summary 535 // 10.7 Computer Examples 535 // 10.7.1 Examples Using R 536 // 10.7.2 Minitab Examples 537 //

10.7.3 SPSS Examples 540 // 10.7.4 SAS Examples 540 // Projects for Chapter 10 545 // CHAPTER 11 Bayesian Estimation Inference 549 // 11.1 Introduction 550 // 11.2 Bayesian Point Estimation 552 // 11.2.1 Criteria for Finding the Bayesian Estimate 558 // 11.3 Bayesian Confidence Interval or Credible Intervals 568 // 11.4 Bayesian Hypothesis Testing 573 // 11.5 Bayesian Decision Theory 576 // 11.6 Chapter Summary 583 // 11.7 Computer Examples 584 // 11.7.1 Examples with R 584 // Projects for Chapter 11 587 // CHAPTER 12 Nonparametric Tests 589 // 12.1 Introduction 590 // 12.2 Nonparametric Confidence Interval 592 // 12.3 Nonparametric Hypothesis Tests for One Sample 597 // 12.3.1 The Sign Test 597 // 12.3.2 Wilcoxon Signed Rank Test 601 // 12.3.3 Dependent Samples: Paired Comparison Tests 606 // 12.4 Nonparametric Hypothesis Tests for Two Independent Samples 609 // 12.4.1 Median Test 609 // 12.4.2 The Wilcoxon Rank Sum Test 613 // 12.5 Nonparametric Hypothesis Tests for ?>2 Samples 618 // 12.5.1 The Kruskal-Wallis Test 618 // 12.5.2 The Friedman Test 621 // 12.6 Chapter Summary 627 // 12.7 Computer Examples 627 // 12.7.1 Examples Using R 628 // 12.7.2 Minitab Examples 630 // 12.7.3 SPSS Examples 632 // 12.7.4 SAS Examples 633 // Projects for Chapter 12 635 // CHAPTER 13 Empirical Methods 639 // 13.1 Introduction 640 // 13.2 The Jackknife Method 640 // 13.3 An Introduction to Bootstrap Methods 645 // 13.3.1 Bootstrap Confidence Intervals 650 // 13.4 The Expectation Maximization Algorithm 651 // 13.5 Introduction to Markov Chain Monte Carlo 662 // 13.5.1 Metropolis Algorithm 666 // 13.5.2 The Metropolis-Hastings Algorithm 670 // 13.5.3 Gibbs Algorithm 673 // 13.5.4 MCMC Issues 676 // 13.6 Chapter Summary 678 // 13.7 Computer Examples 679 // 13.7.1 Examples Using R 679 // 13.7.2 Examples with Minitab 685 // 13.7.3 SAS Examples 686 // Projects for Chapter 13 686 //

CHAPTER 14 Some Issues in Statistical Applications: An Overview 687 // 14.1 Introduction 688 // 14.2 Graphical Methods 689 // 14.3 Outliers 694 // 14.4 Checking Assumptions 699 // 14.4.1 Checking the Assumption of Normality 699 // 14.4.2 Data Transformation 703 // 14.4.3 Test for Equality of Variances 705 // 14.4.4 Test of Independence 709 // 14.5 Modeling Issues 712 // 14.5.1 A Simple Model for Univariate Data 713 // 14.5.2 Modeling Bivariate Data 715 // 14.6 Parametric Versus Nonparametric Analysis 719 // 14.7 Tying it All Together 721 // 14.8 Conclusion 731 // APPENDIX A Set Theory 733 // APPENDIX ? Review of Markov Chains 737 // APPENDIX C Common Probability Distributions 743 // APPENDIX D What is R? 745 // APPENDIX E Probability Tables 747 // References 785

(OCoLC)896980648