Introductory statistics and random phenomena: uncertainty, complexity and chaotic behavior in engineering and science
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Boston [u.a.]
Birkhäuser
1998
|
| Series: | Statistics for industry and technology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XXIV, 509 S. Ill., graph. Darst. |
| ISBN: | 3764340312 0817640312 |
Staff View
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Contents
Preface xi
Introduction xv
Notation and Abbreviations xxiii
I DESCRIPTIVE STATISTICS COMPRESSING DATA 1
1 Why One Needs to Analyze Data 3
1.1 Coin tossing, lottery, and the stock market 3
1.2 Inventory problems in management 9
1.3 Battery life and quality control in manufacturing 10
1.4 Reliability of complex systems 12
1.5 Point processes in time and space 17
1.6 Polls social sciences 21
1.7 Time series 26
1.8 Repeated experiments and testing 29
1.9 Simple chaotic dynamical systems 32
1.10 Complex dynamical systems 39
1.11 Pseudorandom number generators and the Monte Carlo methods 41
1.12 Fractals and image reconstruction 45
1.13 Coding and decoding, unbreakable ciphers 46
1.14 Experiments, exercises, and projects 49
1.15 Bibliographical notes 52
2 Data Representation and Compression 55
2.1 Data types, categorical data 55
2.2 Numerical data: order statistics, median, quantiles 63
2.3 Numerical data: histograms, means, moments 70
2.4 Location, dispersion, and shape parameters 77
v
vi Contents
2.5 Probabilities: a frequentist viewpoint 82
2.6 Multidimensional data: histograms and other graphical represen¬
tations 88
2.7 2 D data: regression and correlations 92
2.8 Fractal data 99
2.9 Measuring information content:entropy 105
2.10 Experiments, exercises, and projects Ill
2.11 Bibliographical notes 115
3 Analytic Representation of Random Experimental Data 119
3.1 Repeated experiments and the law of large numbers 119
3.2 Characteristics of experiments: distribution functions, densities,
means, variances 128
3.3 Uniform distributions, simulation of random quantities, the Monte
Carlo method 136
3.4 Bernoulli and binomial distributions 139
3.5 Rescaling probabilities: Poisson approximation 145
3.6 Stability of Fluctuations Law: Gaussian approximation 152
3.7 How to estimate p in Bernoulli experiments 163
3.8 Other continuous distributions; Gamma function calculus . 171
3.9 Testing the fit of a distribution 185
3.10 Random vectors and multivariate distributions 188
3.11 Experiments, exercises, and projects 196
3.12 Bibliographical notes 198
II MODELING UNCERTAINTY 201
4 Algorithmic Complexity and Random Strings 203
4.1 Heart of randomness: when is random random ? 203
4.2 Computable strings and the Turing machine 207
4.3 Kolmogorov complexity and random strings 212
4.4 Typical sequences: Martin L6f tests of randomness 218
4.5 Stability of subsequences: von Mises randomness 226
4.6 Computable framework of randomness: degrees of irregularity . 228
4.7 Experiments, exercises, and projects 237
4.8 Bibliographical notes 240
5 Statistical Independence and Kolmogorov's Probability Theory 243
5.1 Description of experiments, random variables, and Kolmogorov's
axioms 243
5.2 Uniform discrete distributions and counting 258
5.3 Statistical independence as a model for repeated experiments . . 261
5.4 Expectations and other characteristics of random variables . . . 265
Contents vii
5.4.1 Expectations 265
5.4.2 Expectations of functions of random variables. Variance. 267
5.4.3 Expectations of functions of vectors. Covariance 268
5.4.4 Expectation of the product. Variance of the sum of inde¬
pendent random variables 269
5.4.5 Moments and the moment generating function 272
5.4.6 Expectations of general random variables 275
5.5 Averages of independent random variables 276
5.6 Laws of large numbers and small deviations 281
5.7 Central limit theorem and large deviations 284
5.8 Experiments, exercises, and projects 287
5.9 Bibliographical Notes 292
6 Chaos in Dynamical Systems: How Uncertainty Arises in Scientific
and Engineering Phenomena 293
6.1 Dynamical systems: general concepts and typical examples . . . 293
6.2 Orbits and fixed points 307
6.3 Stability of frequencies and the ergodic theorem 325
6.4 Stability of fluctuations and the central limit theorem 340
6.5 Attractors, fractals, and entropy 349
6.6 Experiments, exercises, and projects 360
6.7 Bibliographical notes 362
III MODEL SPECIFICATION DESIGN OF
EXPERIMENTS 365
7 General Principles of Statistical Analysis 367
7.1 Design of experiments and planning of investigation 367
7.2 Model selection 369
7.3 Determining the method of statistical inference 372
7.3.1 Maximum likelihood estimator (MLE) 373
7.3.2 Least squares estimator (LSE) 376
7.3.3 Method of moments (MM) 381
7.3.4 Concluding remarks 383
7.4 Estimation of fractal dimension 384
7.5 Practical side of data collection and analysis 387
7.6 Experiments, exercises, and projects 389
7.7 Bibliographical notes 390
8 Statistical Inference for Normal Populations 393
8.1 Introduction; parametric inference 393
8.2 Confidence intervals for one sample model 406
8.3 From confidence intervals to hypothesis testing 414
viii Contents
8.4 Statistical inference for two sample normal models 422
8.5 Regression analysis for the normal model 427
8.6 Testing for goodness of fit 435
8.7 Experiments, exercises, and projects 438
8.8 Bibliographical notes 440
9 Analysis of Variance 443
9.1 Single factor ANOVA 443
9.2 Two factor ANOVA 448
9.3 Experiments, exercises, and projects 456
9.4 Bibliographical notes 459
A Uncertainty Principle in Signal Processing and Quantum Mechanics 461
B Fuzzy Systems and Logic 465
C A Critique of Pure Reason 469
D The Remarkable Bernoulli Family 473
E Uncertain Virtual Worlds Mathematica Packages 477
F Tables 497
Index 503 |
| any_adam_object | 1 |
| author | Denker, Manfred 1944- Woyczyński, Wojbor A. 1943- Ycart, Bernard 1958- |
| author_GND | (DE-588)108215253 (DE-588)120518147 (DE-588)120595478 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| isbn | 3764340312 0817640312 |
| language | German |
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| spelling | Denker, Manfred 1944- Verfasser (DE-588)108215253 aut Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science Manfred Denker ; Wojbor A. Woyczyński <<with>> Mathematica uncertain virtual worlds <<by Bernard Ycart>> Boston [u.a.] Birkhäuser 1998 XXIV, 509 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics for industry and technology Literaturangaben Mathematica (Computer file) Estadística matemática Statistiek gtt Stochastische processen gtt Statistik Mathematical statistics Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Woyczyński, Wojbor A. 1943- Verfasser (DE-588)120518147 aut Ycart, Bernard 1958- (DE-588)120595478 aut Mathematica uncertain virtual worlds HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008349798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Denker, Manfred 1944- Woyczyński, Wojbor A. 1943- Ycart, Bernard 1958- Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science Mathematica (Computer file) Estadística matemática Statistiek gtt Stochastische processen gtt Statistik Mathematical statistics Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4079013-7 (DE-588)4056995-0 |
| title | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science |
| title_alt | Mathematica uncertain virtual worlds |
| title_auth | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science |
| title_exact_search | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science |
| title_full | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science Manfred Denker ; Wojbor A. Woyczyński |
| title_fullStr | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science Manfred Denker ; Wojbor A. Woyczyński |
| title_full_unstemmed | Introductory statistics and random phenomena uncertainty, complexity and chaotic behavior in engineering and science Manfred Denker ; Wojbor A. Woyczyński |
| title_short | Introductory statistics and random phenomena |
| title_sort | introductory statistics and random phenomena uncertainty complexity and chaotic behavior in engineering and science |
| title_sub | uncertainty, complexity and chaotic behavior in engineering and science |
| topic | Mathematica (Computer file) Estadística matemática Statistiek gtt Stochastische processen gtt Statistik Mathematical statistics Probabilities Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Mathematica (Computer file) Estadística matemática Statistiek Stochastische processen Statistik Mathematical statistics Probabilities Wahrscheinlichkeitstheorie |
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