From Algorithms to Z-Scores - matloff - University of California, Davis

More documents

Recommendations

Info

vi CONTENTS 5.5.5.1 Density and Properties . . . . . . . . . . . . . . . . . . . . . . . . . 118 5.5.5.2 Example: Network Buffer . . . . . . . . . . . . . . . . . . . . . . . . 119 5.5.5.3 Importance in Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 119 5.5.6 The Beta Family of Distributions . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.6 Choosing a Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 5.7 A General Method for Simulating a Random Variable . . . . . . . . . . . . . . . . . 122 5.8 “Hybrid” Continuous/Discrete Distributions . . . . . . . . . . . . . . . . . . . . . . . 123 6 Stop and Review: Probability Structures 127 7 Covariance and Random Vectors 131 7.1 Measuring Co-variation of Random Variables . . . . . . . . . . . . . . . . . . . . . . 131 7.1.1 Covariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 7.1.2 Example: Variance of Sum of Nonindependent Variables . . . . . . . . . . . . 133 7.1.3 Example: the Committee Example Again . . . . . . . . . . . . . . . . . . . . 133 7.1.4 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 7.1.5 Example: a Catchup Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.2 Sets of Independent Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 135 7.2.1 Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.2.1.1 Expected Values Factor . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.2.1.2 Covariance Is 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 7.2.1.3 Variances Add . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.2.2 Examples Involving Sets of Independent Random Variables . . . . . . . . . . 137 7.2.2.1 Example: Dice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 7.2.2.2 Example: Variance of a Product . . . . . . . . . . . . . . . . . . . . 138 7.2.2.3 Example: Ratio of Independent Geometric Random Variables . . . 138 7.3 Matrix Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
CONTENTS vii 7.3.1 Properties of Mean Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.3.2 Covariance Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.3.3 Example: (X,S) Dice Example Again . . . . . . . . . . . . . . . . . . . . . . . 141 7.3.4 Example: Easy Sum Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.3.5 Example: Dice Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.3.6 Correlation Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 8 Multivariate PMFs and Densities 149 8.1 Multivariate Probability Mass Functions . . . . . . . . . . . . . . . . . . . . . . . . . 149 8.2 Multivariate Densities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.2.1 Motivation and Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 8.2.2 Use of Multivariate Densities in Finding Probabilities and Expected Values . 152 8.2.3 Example: a Triangular Distribution . . . . . . . . . . . . . . . . . . . . . . . 153 8.2.4 Example: Train Rendezvouz . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 8.3 More on Sets of Independent Random Variables . . . . . . . . . . . . . . . . . . . . . 157 8.3.1 Probability Mass Functions and Densities Factor in the Independent Case . . 157 8.3.2 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8.3.3 Example: Ethernet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.3.4 Example: Analysis of Seek Time . . . . . . . . . . . . . . . . . . . . . . . . . 159 8.3.5 Example: Backup Battery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8.3.6 Example: Minima of Uniformly Distributed Random Variables . . . . . . . . 161 8.3.7 Example: Minima of Independent Exponentially Distributed Random Variables161 8.3.8 Example: Computer Worm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 8.3.9 Example: Electronic Components . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3.10 Example: Ethernet Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.4 Example: Finding the Distribution of the Sum of Nonindependent Random Variables 165 8.5 Parametric Families of Multivariate Distributions . . . . . . . . . . . . . . . . . . . . 165
Page 1 and 2: From Algorithms to Z-Scores: Probab
Page 3 and 4: Contents 1 Time Waste Versus Empowe
Page 5 and 6: CONTENTS iii 3.7 A Combinatorial Ex
Page 7: CONTENTS v 5.5.1.3 Example: Modelin
Page 11 and 12: CONTENTS ix 10.1 Sampling Distribut
Page 13 and 14: CONTENTS xi 11.9.4 What to Do Inste
Page 15 and 16: CONTENTS xiii 15.2 Example Applicat
Page 17 and 18: CONTENTS xv 17.2.3 Logistic Regress
Page 19 and 20: CONTENTS xvii 19.2 Simulation of Ra
Page 21 and 22: CONTENTS xix 21.4 Loss Models . . .
Page 23 and 24: Preface Why is this book different
Page 25 and 26: Chapter 1 Time Waste Versus Empower
Page 27 and 28: Chapter 2 Basic Probability Models
Page 29 and 30: 2.2. THE CRUCIAL NOTION OF A REPEAT
Page 31 and 32: 2.3. OUR DEFINITIONS 7 2009, cannot
Page 33 and 34: 2.4. “MAILING TUBES” 9 but in m
Page 35 and 36: 2.5. BASIC PROBABILITY COMPUTATIONS
Page 37 and 38: 2.6. BAYES’ RULE 13 Note by the w
Page 39 and 40: 2.8. SOLUTION STRATEGIES 15 2.8 Sol
Page 41 and 42: 2.10. EXAMPLE: A SIMPLE BOARD GAME
Page 43 and 44: 2.11. EXAMPLE: BUS RIDERSHIP 19 Aga
Page 45 and 46: 2.12. SIMULATION 21 1 # roll d dice
Page 47 and 48: 2.12. SIMULATION 23 So, in evaluati
Page 49 and 50: 2.12. SIMULATION 25 3 count
Page 51 and 52: 2.13. COMBINATORICS-BASED PROBABILI
Page 59 and 60:
Chapter 3 Discrete Random Variables
Page 61 and 62:
3.4. EXPECTED VALUE 37 3.4.1.1 What
Page 63 and 64:
3.4. EXPECTED VALUE 39 So It turns
Page 65 and 66:
3.4. EXPECTED VALUE 41 • For rand
Page 67 and 68:
3.4. EXPECTED VALUE 43 of two rando
Page 69 and 70:
3.5. VARIANCE 45 ance of U is defin
Page 71 and 72:
3.5. VARIANCE 47 for any constant d
Page 73 and 74:
3.7. A COMBINATORIAL EXAMPLE 49 You
Page 75 and 76:
3.8. A USEFUL FACT 51 Note carefull
Page 77 and 78:
3.10. EXPECTED VALUE, ETC. IN THE A
Page 79 and 80:
3.11. DISTRIBUTIONS 55 3.11.1 Examp
Page 81 and 82:
3.12. PARAMETERIC FAMILIES OF PMFS
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
3.13. RECOGNIZING SOME PARAMETRIC D
Page 95 and 96:
3.13. RECOGNIZING SOME PARAMETRIC D
Page 97 and 98:
3.15. A CAUTIONARY TALE 73 T has a
Page 99 and 100:
3.16. WHY NOT JUST DO ALL ANALYSIS
Page 101 and 102:
3.18. RECONCILIATION OF MATH AND IN
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Chapter 4 Introduction to Discrete
Page 109 and 110:
4.3. EXAMPLE: 3-HEADS-IN-A-ROW GAME
Page 111 and 112:
4.4. EXAMPLE: ALOHA 87 The quantity
Page 113 and 114:
4.6. AN INVENTORY MODEL 89 4.6 An I
Page 115 and 116:
Chapter 5 Continuous Probability Mo
Page 117 and 118:
5.3. BUT EQUATION (??) PRESENTS A P
Page 119 and 120:
5.3. BUT EQUATION (??) PRESENTS A P
Page 121 and 122:
5.4. DENSITY FUNCTIONS 97 2(0.1)fX(
Page 123 and 124:
5.4. DENSITY FUNCTIONS 99 5.4.2 Pro
Page 125 and 126:
5.5. FAMOUS PARAMETRIC FAMILIES OF
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Page 143 and 144:
Page 145 and 146:
Page 147 and 148:
5.8. “HYBRID” CONTINUOUS/DISCRE
Page 149 and 150:
5.8. “HYBRID” CONTINUOUS/DISCRE
Page 151 and 152:
Chapter 6 Stop and Review: Probabil
Page 153 and 154:
• famous parametric families of d
Page 155 and 156:
Chapter 7 Covariance and Random Vec
Page 157 and 158:
7.1. MEASURING CO-VARIATION OF RAND
Page 159 and 160:
7.2. SETS OF INDEPENDENT RANDOM VAR
Page 161 and 162:
7.2. SETS OF INDEPENDENT RANDOM VAR
Page 163 and 164:
7.3. MATRIX FORMULATIONS 139 this l
Page 165 and 166:
7.3. MATRIX FORMULATIONS 141 consis
Page 167 and 168:
7.3. MATRIX FORMULATIONS 143 import
Page 169 and 170:
7.3. MATRIX FORMULATIONS 145 since
Page 171 and 172:
7.3. MATRIX FORMULATIONS 147 minimi
Page 173 and 174:
Chapter 8 Multivariate PMFs and Den
Page 175 and 176:
8.1. MULTIVARIATE PROBABILITY MASS
Page 177 and 178:
8.2. MULTIVARIATE DENSITIES 153 So,
Page 179 and 180:
8.2. MULTIVARIATE DENSITIES 155 we
Page 181 and 182:
8.3. MORE ON SETS OF INDEPENDENT RA
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Page 189 and 190:
8.4. EXAMPLE: FINDING THE DISTRIBUT
Page 191 and 192:
8.5. PARAMETRIC FAMILIES OF MULTIVA
Page 193 and 194:
Page 195 and 196:
Page 197 and 198:
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Chapter 9 Introduction to Continuou
Page 209 and 210:
9.1. MEMORYLESS PROPERTY OF EXPONEN
Page 211 and 212:
9.3. HOLDING-TIME DISTRIBUTION 187
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Chapter 10 Introduction to Confiden
Page 219 and 220:
10.1. SAMPLING DISTRIBUTIONS 195 Wh
Page 221 and 222:
10.1. SAMPLING DISTRIBUTIONS 197 Ap
Page 223 and 224:
10.3. CONFIDENCE INTERVALS FOR MEAN
Page 225 and 226:
10.4. MEANING OF CONFIDENCE INTERVA
Page 227 and 228:
10.5. GENERAL FORMATION OF CONFIDEN
Page 229 and 230:
10.7. CONFIDENCE INTERVALS FOR PROP
Page 231 and 232:
10.7. CONFIDENCE INTERVALS FOR PROP
Page 233 and 234:
10.8. CONFIDENCE INTERVALS FOR DIFF
Page 235 and 236:
Page 237 and 238:
Page 239 and 240:
10.10. R COMPUTATION 215 algebra, w
Page 241 and 242:
10.13. OTHER CONFIDENCE LEVELS 217
Page 243 and 244:
10.14. ONE MORE TIME: WHY DO WE USE
Page 245 and 246:
Chapter 11 Introduction to Signific
Page 247 and 248:
11.2. GENERAL TESTING BASED ON NORM
Page 249 and 250:
11.5. ONE-SIDED HA 225 By checking
Page 251 and 252:
11.6. EXACT TESTS 227 It is natural
Page 253 and 254:
11.8. THE POWER OF A TEST 229 11.8
Page 255 and 256:
11.9. WHAT’S WRONG WITH SIGNIFICA
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Chapter 12 General Statistical Esti
Page 263 and 264:
12.1. GENERAL METHODS OF PARAMETRIC
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
12.2. BIAS AND VARIANCE 247 people,
Page 273 and 274:
12.2. BIAS AND VARIANCE 249 Moreove
Page 275 and 276:
12.3. MORE ON THE ISSUE OF INDEPEND
Page 277 and 278:
12.4. NONPARAMETRIC DISTRIBUTION ES
Page 279 and 280:
Page 281 and 282:
Page 283 and 284:
12.5. BAYESIAN METHODS 259 his plan
Page 285 and 286:
12.5. BAYESIAN METHODS 261 it now b
Page 287 and 288:
12.5. BAYESIAN METHODS 263 number
Page 289 and 290:
12.5. BAYESIAN METHODS 265 (b) ˆp,
Page 291 and 292:
Chapter 13 Simultaneous Inference M
Page 293 and 294:
13.2. SCHEFFE’S METHOD 269 You ca
Page 295 and 296:
13.4. OTHER METHODS FOR SIMULTANEOU
Page 297 and 298:
Chapter 14 Introduction to Model Bu
Page 299 and 300:
14.1. “DESPERATE FOR DATA” 275
Page 301 and 302:
14.1. “DESPERATE FOR DATA” 277
Page 303 and 304:
14.2. ASSESSING “GOODNESS OF FIT
Page 305 and 306:
14.4. ROBUSTNESS 281 bin width, or
Page 307 and 308:
14.5. REAL POPULATIONS AND CONCEPTU
Page 309 and 310:
Chapter 15 Relations Among Variable
Page 311 and 312:
15.3. ADJUSTING FOR COVARIATES 287
Page 313 and 314:
15.6. ESTIMATING THAT RELATIONSHIP
Page 315 and 316:
15.6. ESTIMATING THAT RELATIONSHIP
Page 317 and 318:
15.7. EXAMPLE: BASEBALL DATA 293
Page 319 and 320:
15.9. EXAMPLE: BASEBALL DATA (CONT
Page 321 and 322:
15.11. PREDICTION 297 matter, it ma
Page 323 and 324:
15.12. PARAMETRIC ESTIMATION OF LIN
Page 325 and 326:
15.12. PARAMETRIC ESTIMATION OF LIN
Page 327 and 328:
15.14. DUMMY VARIABLES 303 15.14 Du
Page 329 and 330:
15.16. WHAT DOES IT ALL MEAN?—EFF
Page 331 and 332:
15.17. MODEL SELECTION 307 But look
Page 333 and 334:
15.17. MODEL SELECTION 309 Foundati
Page 335 and 336:
15.18. WHAT ABOUT THE ASSUMPTIONS?
Page 337 and 338:
15.19. CASE STUDIES 313 have an und
Page 339 and 340:
15.19. CASE STUDIES 315 Exercises N
Page 341 and 342:
15.19. CASE STUDIES 317 8. Consider
Page 343 and 344:
Chapter 16 Advanced Statistical Est
Page 345 and 346:
16.2. THE DELTA METHOD: CONFIDENCE
Page 347 and 348:
Page 349 and 350:
Page 351 and 352:
Page 353 and 354:
16.3. THE BOOTSTRAP METHOD FOR FORM
Page 355 and 356:
16.3. THE BOOTSTRAP METHOD FOR FORM
Page 357 and 358:
Chapter 17 Relations Among Variable
Page 359 and 360:
17.2. THE CLASSIFICATION PROBLEM 33
Page 361 and 362:
Page 363 and 364:
Page 365 and 366:
17.3. NONPARAMETRIC ESTIMATION OF R
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
Page 375 and 376:
17.4. SYMMETRIC RELATIONS AMONG SEV
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
17.5. SIMPSON’S (NON-)PARADOX 357
Page 383 and 384:
17.5. SIMPSON’S (NON-)PARADOX 359
Page 385 and 386:
Chapter 18 Describing “Failure”
Page 387 and 388:
18.2. A CAUTIONARY TALE: THE BUS PA
Page 389 and 390:
18.2. A CAUTIONARY TALE: THE BUS PA
Page 391 and 392:
18.3. RESIDUAL-LIFE DISTRIBUTION 36
Page 393 and 394:
Page 395 and 396:
Page 397 and 398:
Page 399 and 400:
Chapter 19 Advanced Multivariate Me
Page 401 and 402:
19.1. CONDITIONAL DISTRIBUTIONS 377
Page 403 and 404:
Page 405 and 406:
Page 407 and 408:
19.3. MIXTURE MODELS 383 Now that w
Page 409 and 410:
19.4. TRANSFORM METHODS 385 Thus an
Page 411 and 412:
19.4. TRANSFORM METHODS 387 19.4.2
Page 413 and 414:
19.4. TRANSFORM METHODS 389 transfo
Page 415 and 416:
19.5. VECTOR SPACE INTERPRETATIONS
Page 417 and 418:
19.7. CONDITIONAL EXPECTATION AS A
Page 419 and 420:
19.8. PROOF OF THE LAW OF TOTAL EXP
Page 421 and 422:
19.8. PROOF OF THE LAW OF TOTAL EXP
Page 423 and 424:
Chapter 20 Markov Chains One of the
Page 425 and 426:
20.1. DISCRETE-TIME MARKOV CHAINS 4
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
Page 433 and 434:
Page 435 and 436:
Page 437 and 438:
Page 439 and 440:
20.2. SIMULATION OF MARKOV CHAINS 4
Page 441 and 442:
20.4. CONTINUOUS-TIME MARKOV CHAINS
Page 443 and 444:
20.5. HITTING TIMES ETC. 419 least
Page 445 and 446:
20.5. HITTING TIMES ETC. 421 First
Page 447 and 448:
20.5. HITTING TIMES ETC. 423 valued
Page 449 and 450:
20.5. HITTING TIMES ETC. 425 summon
Page 451 and 452:
Chapter 21 Introduction to Queuing
Page 453 and 454:
21.2. M/M/1 429 busy for approximat
Page 455 and 456:
21.2. M/M/1 431 • Due to the memo
Page 457 and 458:
21.3. MULTI-SERVER MODELS 433 Recal
Page 459 and 460:
21.4. LOSS MODELS 435 1 = i,j,k π
Page 461 and 462:
21.5. NONEXPONENTIAL SERVICE TIMES
Page 463 and 464:
21.6. REVERSED MARKOV CHAINS 439 So
Page 465 and 466:
21.6. REVERSED MARKOV CHAINS 441 21
Page 467 and 468:
21.6. REVERSED MARKOV CHAINS 443 Re
Page 469 and 470:
21.7. NETWORKS OF QUEUES 445 • Gi
Page 471 and 472:
21.7. NETWORKS OF QUEUES 447 Let Li
Page 473 and 474:
Appendix A Review of Matrix Algebra
Page 475 and 476:
A.2. MATRIX TRANSPOSE 451 • Matri
Page 477 and 478:
A.6. EIGENVALUES AND EIGENVECTORS 4
Page 479 and 480:
Appendix B R Quick Start Here we pr
Page 481 and 482:
B.3. FIRST SAMPLE PROGRAMMING SESSI
Page 483 and 484:
B.4. SECOND SAMPLE PROGRAMMING SESS
Page 485 and 486:
B.4. SECOND SAMPLE PROGRAMMING SESS
Page 487 and 488:
B.6. COMPLEX NUMBERS 463 B.6 Comple
show all

From Algorithms to Z-Scores - matloff - University of California, Davis

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?