Probability, Statistics, and Decision for Civil Engineers

Probability, Statistics, and Decision for Civil Engineers

by Jack R Benjamin PhD, C. Allin Cornell PhD

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Product Details

ISBN-13: 9780486780726
Publisher: Dover Publications
Publication date: 07/16/2014
Series: Dover Books on Engineering
Pages: 704
Sales rank: 545,323
Product dimensions: 6.00(w) x 8.80(h) x 1.50(d)
Age Range: 18 Years

About the Author


C. Allin Cornell (1938–2007) was Professor Emeritus of Civil and Environmental Engineering at Stanford University. He helped pioneer the field of Probabilistic Seismic Hazard Analysis (PSHA), which quantifies and predicts the risks and hazards of earthquakes.
Jack R. Benjamin (1917–98) was Professor Emeritus of Civil and Environmental Engineering at Stanford University, where he taught for 25 years.

Table of Contents

Preface vii

Introduction 1

Chapter 1 Data Reduction 4

1.1 Graphical Displays 5

1.2 Numerical Summaries 9

1.3 Data Observed in Pairs 14

1.4 Summary for Chapter1 17

Chapter 2 Elements of Probability Theory 32

2.1 Random Events 33

2.1.1 Sample Space and Events 33

2.1.2 Probability Measure 40

2.1.3 Simple Probabilities of Events 44

2.1.4 Summary 69

2.2 Random Variables and Distributions 69

2.2.1 Random Variables 70

2.2.2 Jointly Distributed Random Variables 83

2.3 Derlved Distributions 100

2.3.1 One-variable Transformations: Y=g(X) 101

2.3.2 Functions of Two Random Variables 112

2.3.3 Elementary Simulation 124

2.3.4 Summary 133

2.4 Moments and Expectation 134

2.4.1 Moments of a Random Variable 135

2.4.2 Expectation of a Function of a Random Variable 143

2.4.3 Expectation and Jointly Distributed Random Variables 158

2.4.4 Approximate Moments and Distributions of Functions 180

2.4.5 Summary 186

2.5 Summary for Chapter2 188

Chapter 3 Common Probabilistic Models 220

3.1 Models from Simple Discrete Random Trials 221

3.1.1 A Single Trials: the Bernoulli Distribution 221

3.1.2 Repeated Trials: the Binomial Distribution 223

3.1.3 Repeated Trials: the Geometric and Negative Binomial Distributions 228

3.1.4 Summary 235

3.2 Modeles from Random Occurrences 236

3.2.1 Counting Events: the Poisson Distribution 236

3.2.2 Time between Events: the Exponential Distributions 242

3.2.3 Time to the kth Event: the Gamma Distribution 245

3.2.4 Summary 249

3.3 Models from Limiting Cases 249

3.3.1 The Model of Sums: the Normal Distribution 249

3.3.2 The Model of Products: the Lognormal Distribution 262

3.3.3 The Model of Extremes: the Extreme Value Distributions 271

3.3.4 Summary 285

3.4 Additional Common Distributions 286

3.4.1 The Equally Likely Model: the Rectangular or Uniform Distribution 286

3.4.2 The Beta Distribution 287

3.4.3 Sorne Normal Related Distributions: Chi-square, Chi, t, and F 292

3.4.4 Summary 301

3.5 Modefied Distributions 302

3.5.1 Shifted and Transformed Distributions 302

3.5.2 Truncated and Censored Distributions 304

3.5.3 Compound Distributions 306

3.5.4 Summary 311

3.6 Multivariate Models 312

3.6.1 Counting Multiple Events: the Multinomial Distribution 312

3.6.2 The Multivariate Normal Distribution 314

3.6.3 Summary 321

3.7 Markov Chains 321

3.7.1 Simple Markov Chains 322

3.7.2 Two-state Homogeneous Chains 330

3.7.3 Multistate Markov Chains 336

3.7.4 Summary 347

3.8 Summary for Chapter3 348

Chapter 4 Probabilistic Models and Observed Data 370

4.1 Estimation of Model Parameters 372

4.1.1 The Method of Moments 372

4.1.2 The Properties of Estimators: Their First-and Second-order Moments 376

4.1.3 The Distributions of Estimators and Confidence-interval Estimation 383

4.1.4 The Method of Maximum Likelihood 396

4.1.5 Summary 402

4.2 Significance Testing 403

4.2.1 Hypothesis Testing 404

4.2.2 Some Common Hypothesis Tests 409

4.2.3 Summary 418

4.3 Statistical Analysis of Linear Models 419

4.3.1 Linear Models 419

4.3.2 Statistical Analysis of Simple Linear Models 428

4.3.3 Summary 439

4.4 Model Verification 440

4.4.1 Comparing Shapes: Histograms and Probability Paper 440

4.4.2 "Goodness-of-fit" Significance Tests 459

4.4.3 Summary 475

4.5 Empirical Selection of Models 475

4.5.1 Model Selection: Illustration l, Loading Times 476

4.5.2 Model Selection: Illustration ll, Maximum Annual Flows 482

4.5.3 Summary 498

4.6 Summary of Chapter4 499

Chapter 5 Elementary Bayesian Decision Theory 524

5.1 Decisions with Given Information 526

5.1.1 The Decision Model 526

5.1.2 Expected-value Decisions 531

5.1.3 Probability Assignments 541

5.1.4 Analysis of the Decision Tree with Given Information 544

5.1.5 Summary 554

5.2 Terminal Analysis 555

5.2.1 Decision Analysis Given New Information 555

5.2.2 Summary 570

5.3 Preposterior Analysis 570

5.3.1 The Complete Decision Model 571

5.3.2 Summary 581

5.4 Summary for Chapter5 581

Chapter 6 Decision Analysis of Independent Random Processes 595

6.1 The Model and Its Prior Analysis 596

6.1.1 Prior Analysis of the Special Problem u(a,X) 598

6.1.2 More General Relationships between the Process and the State of Interest 607

6.1.3 Summary 613

6.2 Terminal Analysis Given Observations of the Process 613

6.2.1 The General Case 614

6.2.2 Data-based Decisions: Diffuse Priors 620

6.2.3 Use of Conjugate Priors 625

6.2.4 Summary 631

6.3 The Bayesian Distribution of a Random Variable 632

6.3.1 The Simple Case: X Only 632

6.3.2 The General Case Y=h(X1, X2,....X3) 637

6.3.3 Summary 641

6.4 Summary of Chapter6 641

Appendix A Tables 653

Table A.1 Values of the Standardized Normal Distribution 654

Table A.2 Tables for Evaluation of the CDF of the X2, Gamma, and Poisson Distributions 656

Table A.3 Cumulative Distribution of Student's t Distributon 662

Table A.4 Properties of Some Standardized Beta Distributions 665

Table A.5 Values of the Standardized Type I Extreme-value Distribution 666

Table A.6 F Distribution; Value of z such that Fz(z)=0.95 667

Table A.7 Critical Statistic for the Kolmogorov-Smirnov Goodness-of-Fit Test 668

Table A.8 Table of Random Digits 668

Appendix B Derivation of the Asymptotic Extreme-value Distribution 670

Name Index 673

Subject Index 677

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