Introductory Statistics and Random Phenomena,9780817640316

Introductory Statistics and Random Phenomena

by ; ;
ISBN13: 9780817640316
ISBN10: 0817640312
Format: Hardcover
Pub. Date: 1999-03-01
Publisher(s): Birkhauser
List Price: $104.99

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Table of Contents

Preface xi(4)
Introduction xv(8)
Notation and Abbreviations xxiii
I DESCRIPTIVE STATISTICS-COMPRESSING DATA 1(200)
1 Why One Needs to Analyze Data
3(52)
1.1 Coin tossing, lottery, and the stock market
3(6)
1.2 Inventory problems in management
9(1)
1.3 Battery life and quality control in manufacturing
10(2)
1.4 Reliability of complex systems
12(5)
1.5 Point processes in time and space
17(4)
1.6 Polls-social sciences
21(5)
1.7 Time series
26(3)
1.8 Repeated experiments and testing
29(3)
1.9 Simple chaotic dynamical systems
32(7)
1.10 Complex dynamical systems
39(2)
1.11 Pseudorandom number generators and the Monte-Carlo methods
41(4)
1.12 Fractals and image reconstruction
45(1)
1.13 Coding and decoding, unbreakable ciphers
46(3)
1.14 Experiments, exercises, and projects
49(3)
1.15 Bibliographical notes
52(3)
2 Data Representation and Compression
55(64)
2.1 Data types, categorical data
55(8)
2.2 Numerical data: order statistics, median, quantiles
63(7)
2.3 Numerical data: histograms, means, moments
70(7)
2.4 Location, dispersion, and shape parameters
77(5)
2.5 Probabilities: a frequentist viewpoint
82(6)
2.6 Multidimensional data: histograms and other graphical representations
88(4)
2.7 2-D data: regression and correlations
92(7)
2.8 Fractal data
99(6)
2.9 Measuring information content: entropy
105(6)
2.10 Experiments, exercises, and projects
111(4)
2.11 Bibliographical notes
115(4)
3 Analytic Representation of Random Experimental Data
119(82)
3.1 Repeated experiments and the law of large numbers
119(9)
3.2 Characteristics of experiments: distribution functions, densities, means, variances
128(8)
3.3 Uniform distributions, simulation of random quantities, the Monte Carlo method
136(3)
3.4 Bernoulli and binomial distributions
139(6)
3.5 Rescaling probabilities: Poisson approximation
145(7)
3.6 Stability of Fluctuations Law: Gaussian approximation
152(11)
3.7 How to estimate p in Bernoulli experiments
163(8)
3.8 Other continuous distributions; Gamma function calculus
171(14)
3.9 Testing the fit of a distribution
185(3)
3.10 Random vectors and multivariate distributions
188(8)
3.11 Experiments, exercises, and projects
196(2)
3.12 Bibliographical notes
198(3)
II MODELING UNCERTAINTY 201(164)
4 Algorithmic Complexity and Random Strings
203(40)
4.1 Heart of randomness: when is random -- random?
203(4)
4.2 Computable strings and the Turing machine
207(5)
4.3 Kolmogorov complexity and random strings
212(6)
4.4 Typical sequences: Martin-Lof tests of randomness
218(8)
4.5 Stability of subsequences: von Mises randomness
226(2)
4.6 Computable framework of randomness: degrees of irregularity
228(9)
4.7 Experiments, exercises, and projects
237(3)
4.8 Bibliographical notes
240(3)
5 Statistical Independence and Kolmogorov's Probability Theory
243(50)
5.1 Description of experiments, random variables, and Kolmogorov's axioms
243(15)
5.2 Uniform discrete distributions and counting
258(3)
5.3 Statistical independence as a model for repeated experiments
261(4)
5.4 Expectations and other characteristics of random variables
265(11)
5.4.1 Expectations
265(2)
5.4.2 Expectations of functions of random variables. Variance
267(1)
5.4.3 Expectations of functions of vectors. Covariance
268(1)
5.4.4 Expectation of the product. Variance of the sum of independent random variables
269(3)
5.4.5 Moments and the moment generating function
272(3)
5.4.6 Expectations of general random variables
275(1)
5.5 Averages of independent random variables
276(5)
5.6 Laws of large numbers and small deviations
281(3)
5.7 Central limit theorem and large deviations
284(3)
5.8 Experiments, exercises, and projects
287(5)
5.9 Bibliographical Notes
292(1)
6 Chaos in Dynamical Systems: How Uncertainty Arises in Scientific and Engineering Phenomena
293(72)
6.1 Dynamical systems: general concepts and typical examples
293(14)
6.2 Orbits and fixed points
307(18)
6.3 Stability of frequencies and the ergodic theorem
325(15)
6.4 Stability of fluctuations and the central limit theorem
340(9)
6.5 Attractors, fractals, and entropy
349(11)
6.6 Experiments, exercises, and projects
360(2)
6.7 Bibliographical notes
362(3)
III MODEL SPECIFICATION-DESIGN OF EXPERIMENTS 365(138)
7 General Principles of Statistical Analysis
367(26)
7.1 Design of experiments and planning of investigation
367(2)
7.2 Model selection
369(3)
7.3 Determining the method of statistical inference
372(12)
7.3.1 Maximum likelihood estimator (MLE)
373(3)
7.3.2 Least squares estimator (LSE)
376(5)
7.3.3 Method of moments (MM)
381(2)
7.3.4 Concluding remarks
383(1)
7.4 Estimation of fractal dimension
384(3)
7.5 Practical side of data collection and analysis
387(2)
7.6 Experiments, exercises, and projects
389(1)
7.7 Bibliographical notes
390(3)
8 Statistical Inference for Normal Populations
393(50)
8.1 Introduction; parametric inference
393(13)
8.2 Confidence intervals for one-sample model
406(8)
8.3 From confidence intervals to hypothesis testing
414(8)
8.4 Statistical inference for two-sample normal models
422(5)
8.5 Regression analysis for the normal model
427(8)
8.6 Testing for goodness-of-fit
435(3)
8.7 Experiments, exercises, and projects
438(2)
8.8 Bibliographical notes
440(3)
9 Analysis of Variance
443(18)
9.1 Single-factor ANOVA
443(5)
9.2 Two-factor ANOVA
448(8)
9.3 Experiments, exercises, and projects
456(3)
9.4 Bibliographical notes
459(2)
A Uncertainty Principle in Signal Processing and Quantum Mechanics
461(4)
B Fuzzy Systems and Logic
465(4)
C A Critique of Pure Reason
469(4)
D The Remarkable Bernoulli Family
473(4)
E Uncertain Virtual Worlds Mathematica Packages
477(20)
F Tables
497(6)
Index 503

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