Applied Statistics for Civil and Environmental Engineers

Contents......Page 6
Preface to the First Edition......Page 15
Preface to the Second Edition......Page 17
Introduction......Page 20
1.1 Graphical Representation......Page 22
1.1.2 Dot diagram......Page 23
1.1.3 Histogram......Page 24
1.1.4 Frequency polygon......Page 27
1.1.5 Cumulative relative frequency diagram......Page 28
1.1.6 Duration curves......Page 29
1.2 Numerical Summaries of Data......Page 30
1.2.1 Measures of central tendency......Page 31
1.2.2 Measures of dispersion......Page 34
1.2.5 Summary of Section 1.2......Page 38
1.3.1 Stem-and-leaf plot......Page 39
1.3.2 Box plot......Page 41
1.4.1 Correlation and graphical plots......Page 42
1.4.2 Covariance and the correlation coefficient......Page 43
1.4.3 Q-Q plots......Page 45
1.5 Summary for Chapter 1......Page 46
References......Page 47
Problems......Page 48
2 Basic Probability Concepts......Page 57
2.1.1 Sample space and events......Page 58
2.1.2 The null event, intersection, and union......Page 60
2.1.3 Venn diagram and event space......Page 62
2.1.4 Summary of Section 2.1......Page 68
2.2.1 Interpretations of probability......Page 69
2.2.2 Probability axioms......Page 71
2.2.3 Addition rule......Page 72
2.2.4 Further properties of probability functions......Page 74
2.2.5 Conditional probability and multiplication rule......Page 75
2.2.6 Stochastic independence......Page 80
2.2.7 Total probability and Bayes’ theorems......Page 84
2.3 Summary for Chapter 2......Page 91
References......Page 92
Problems......Page 93
3.1.1 Random variables......Page 102
3.1.2 Probability mass function......Page 103
3.1.3 Cumulative distribution function of a discrete random variable......Page 104
3.1.4 Probability density function......Page 105
3.1.5 Cumulative distribution function of a continuous random variable......Page 107
3.2.1 Expectation and other population measures......Page 109
3.2.2 Generating functions......Page 118
3.2.3 Estimation of parameters......Page 122
3.3 Multiple Random Variables......Page 131
3.3.1 Joint probability distributions of discrete variables......Page 132
3.3.2 Joint probability distributions of continuous variables......Page 137
3.3.3 Properties of multiple variables......Page 143
3.4 Associated Random Variables and Probabilities......Page 151
3.4.1 Functions of a random variable......Page 152
3.4.2 Functions of two or more variables......Page 154
3.4.3 Properties of derived variables......Page 162
3.4.4 Compound variables......Page 170
3.5 Copulas......Page 173
References......Page 176
Problems......Page 179
4.1 Discrete Distributions......Page 184
4.1.1 Bernoulli distribution......Page 185
4.1.2 Binomial distribution......Page 186
4.1.3 Poisson distribution......Page 190
4.1.4 Geometric and negative binomial distributions......Page 200
4.1.5 Log-series distribution......Page 204
4.1.6 Multinomial distribution......Page 206
4.1.7 Hypergeometric distribution......Page 208
4.1.8 Summary of Section 4.1......Page 211
4.2.1 Uniform distribution......Page 213
4.2.2 Exponential distribution......Page 215
4.2.3 Erlang and gamma distribution......Page 219
4.2.4 Beta distribution......Page 222
4.2.5 Weibull distribution......Page 224
4.2.6 Normal distribution......Page 228
4.2.7 Lognormal distribution......Page 234
4.3 Multivariate Distributions......Page 236
4.3.1 Bivariate normal distribution......Page 238
4.4 Summary for Chapter 4......Page 241
References......Page 242
Problems......Page 243
5.1 A Review of Terms Related to Random Sampling......Page 249
5.2.1 Unbiasedness......Page 250
5.2.3 Minimum variance......Page 251
5.2.5 Sufficiency......Page 253
5.2.6 Summary of Section 5.2......Page 254
5.3.1 Confidence interval estimation of the mean when the standard deviation is known......Page 255
5.3.2 Confidence interval estimation of the mean when the standard deviation is unknown......Page 258
5.3.4 Sampling distribution of differences and sums of statistics......Page 261
5.3.5 Interval estimation for the variance: chi-squared distribution......Page 262
5.4 Hypothesis Testing......Page 266
5.4.1 Procedure for testing......Page 267
5.4.2 Probabilities of Type I and Type II errors and the power function......Page 273
5.4.3 Neyman-Pearson lemma......Page 275
5.4.4 Tests of hypotheses involving the variance......Page 276
5.4.5 The F distribution and its use......Page 277
5.4.6 Summary of Section 5.4......Page 278
5.5 Nonparametric Methods......Page 279
5.5.1 Sign test applied to the median......Page 280
5.5.2 Wilcoxon signed-rank test for association of paired observations......Page 281
5.5.3 Kruskal-Wallis test for paired observations in k samples......Page 283
5.5.4 Tests on randomness: runs test......Page 286
5.5.5 Spearman’s rank correlation coefficient......Page 287
5.5.6 Summary of Section 5.5......Page 288
5.6 Goodness-of-Fit Tests......Page 289
5.6.1 Chi-squared goodness-of-fit test......Page 290
5.6.2 Kolmogorov-Smirnov goodness-of-fit test......Page 292
5.6.3 Kolmogorov-Smirnov two-sample test......Page 293
5.6.4 Anderson-Darling goodness-of-fit test......Page 296
5.6.5 Other methods for testing the goodness-of-fit to a normal distribution......Page 300
5.6.6 Summary of Section 5.6......Page 301
5.7 Analysis of Variance......Page 302
5.7.1 One-way analysis of variance......Page 303
5.7.2 Two-way analysis of variance......Page 307
5.7.3 Summary of Section 5.7......Page 313
5.8 Probability Plotting Methods and Visual Aids......Page 314
5.8.1 Probability plotting for uniform distribution......Page 315
5.8.2 Probability plotting for normal distribution......Page 316
5.8.3 Probability plotting for Gumbel or EV1 distribution......Page 319
5.8.4 Probability plotting of other distributions......Page 320
5.8.5 Visual fitting methods based on the histogram......Page 322
5.9 Identification and Accommodation of Outliers......Page 324
5.9.1 Hypothesis tests......Page 325
5.9.2 Test statistics for detection of outliers......Page 326
5.9.3 Dealing with nonnormal data......Page 328
5.9.4 Estimation of probabilities of extreme events when outliers are present......Page 330
5.10 Summary of Chapter 5......Page 331
References......Page 332
Problems......Page 335
6 Methods of Regression and Multivariate Analysis......Page 345
6.1 Simple Linear Regression......Page 346
6.1.1 Estimates of the parameters......Page 347
6.1.2 Properties of the estimators and errors......Page 351
6.1.3 Tests of significance and confidence intervals......Page 356
6.1.4 The bivariate normal model and correlation......Page 358
6.2 Multiple Linear Regression......Page 361
6.2.2 Linear least squares solutions using the matrix method......Page 362
6.2.3 Properties of least squares estimators and error variance......Page 365
6.2.4 Model testing......Page 369
6.2.5 Model adequacy......Page 374
6.2.6 Residual plots......Page 375
6.2.7 Influential observations and outliers in regression......Page 377
6.2.8 Transformations......Page 384
6.2.9 Confidence intervals on mean response and prediction......Page 385
6.2.10 Ridge regression......Page 387
6.2.11 Other methods and discussion of Section 6.2......Page 389
6.3.1 Principal components analysis......Page 392
6.3.2 Factor analysis......Page 398
6.3.3 Cluster analysis......Page 402
6.3.4 Other methods and summary of Section 6.3......Page 404
6.4 Spatial Correlation......Page 405
6.4.2 Spatial correlation and the semivariogram......Page 406
6.4.3 Some semivariogram models and physical aspects......Page 408
6.4.4 Spatial interpolations and Kriging......Page 411
6.5 Summary of Chapter 6......Page 413
References......Page 414
Problems......Page 417
7 Frequency Analysis of Extreme Events......Page 424
7.1.1 Definitions and distributions......Page 425
7.1.2 Functions of order statistics......Page 428
7.1.3 Expected value and variance of order statistics......Page 430
7.2.1 Basic concepts of extreme value theory......Page 434
7.2.2 Gumbel distribution......Page 441
7.2.3 Fr´ echet distribution......Page 448
7.2.4 Weibull distribution as an extreme value model......Page 451
7.2.5 General extreme value distribution......Page 454
7.2.6 Contagious extreme value distributions......Page 458
7.2.7 Use of other distributions as extreme value models......Page 464
7.2.8 Summary of Section 7.2......Page 469
7.3.1 Floods, storms, and droughts......Page 472
7.3.2 Earthquakes and volcanic eruptions......Page 480
7.3.3 Winds......Page 484
7.3.4 Sea levels and highest sea waves......Page 489
7.3.5 Summary of Section 7.3......Page 492
References......Page 493
Problems......Page 497
8 Simulation Techniques for Design......Page 506
8.1.1 Statistical experiments......Page 507
8.1.2 Probability integral transform......Page 512
8.1.3 Sample size and accuracy of Monte Carlo experiments......Page 514
8.2.1 Random outcomes from standard uniform variates......Page 520
8.2.2 Random outcomes from continuous variates......Page 525
8.2.3 Random outcomes from discrete variates......Page 530
8.2.4 Random outcomes from jointly distributed variates......Page 532
8.3.1 Distributions of derived design variates......Page 533
8.3.2 Sampling statistics......Page 536
8.3.3 Simulation of time- or space-varying systems......Page 538
8.3.4 Design alternatives and optimal design......Page 543
8.4 Sensitivity and Uncertainty Analysis......Page 549
References......Page 550
Problems......Page 552
9 Risk and Reliability Analysis......Page 560
9.1.1 Factors of safety......Page 561
9.1.2 Safety margin......Page 566
9.1.3 Reliability index......Page 569
9.1.4 Performance function and limiting state......Page 577
9.1.5 Further practical solutions......Page 587
9.2 Multiple Failure Modes......Page 596
9.2.1 Independent failure modes......Page 597
9.2.2 Mutually dependent failure modes 584......Page 603
9.3.1 Reliability limits 592......Page 611
9.3.2 Bayesian revision of reliability......Page 612
9.4.1 Failure process and survival time......Page 616
9.4.2 Hazard function......Page 621
9.4.3 Reliable life......Page 624
9.5 Reliability-Based Design......Page 625
9.6 Summary for Chapter 9......Page 631
References......Page 632
Problems......Page 634
10 Bayesian Decision Methods and Parameter Uncertainty......Page 642
10.1.1 Bayes’ rules......Page 643
10.1.2 Decision trees 627......Page 646
10.1.3 The minimax solution......Page 649
10.2 Posterior Bayesian Decision Analysis......Page 651
10.2.1 Subjective probabilities......Page 652
10.2.2 Loss and utility functions......Page 653
10.2.3 The discrete case......Page 654
10.2.4 Inference with conditional binomial and prior beta......Page 655
10.2.5 Poisson hazards and gamma prior......Page 657
10.2.6 Inferences with normal distribution......Page 658
10.2.7 Likelihood ratio testing......Page 661
10.3 Markov Chain Monte Carlo Methods......Page 662
10.4 James-Stein Estimators......Page 669
References......Page 672
Problems......Page 675
A.3 Derivation of the Poisson distribution......Page 678
A.4 Derivation of the normal distribution......Page 679
A.5 MGF of the normal distribution 661......Page 680
A.6 Central limit theorem......Page 681
A.7 Pdf of Student’s T distribution......Page 682
A.9 Wilcoxon signed-rank test: mean and variance of the test statistic......Page 683
A.10 Spearman’s rank correlation coefficient......Page 684
Appendix B: Glossary of Symbols 667......Page 686
Appendix C: Tables of Selected Distributions 673......Page 692
Appendix D: Brief Answers to Selected Problems......Page 703
Appendix E: Data Lists 687......Page 706
Index......Page 726