Stable chaos: An introd. to statistical control
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Morristown, N.J.
General Learning Pr.
1971
|
| Series: | D.H.Mark publication.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV,582 S. |
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| 245 | 1 | 0 | |a Stable chaos |b An introd. to statistical control |
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| adam_text | Contents
Part I PROBABILITY AND RANDOM VARIABLES
Chapter I Stable Chaos and Statistical Control: Frequency Distributions 1
1.1 A Basic Statistical Concept 1
1.2 Illustrations and Applications 2
1.3 Statistics as the Study of Populations 7
1.4 The Frequency Distribution: A Basic Statistical Tool 8
1.5 The Calculus of Relative Frequencies 13
1.6 From Relative Frequencies to Probabilities 18
Chapter II Equally Probable Events: Random Numbers 24
2.1 Laplace s Formulation 24
2.2 Examples Involving Equally Probable Events 25
2.3 Some Empirical Evidence 34
2.4 Random Numbers 37
2.5 Pseudorandom Numbers 40
2.6 Testing Random Numbers: Introductory Remarks 41
2.7 Random Numbers and Equally Probable Samples 43
Chapter HI The Frequency Theory, Randomness, and Independence 48
3.1 The Frequency Theory 48
3.2 Disorder and Relative Randomness in Infinite Sequences 51
3.3 The Normal Sequency: a Step toward Universal Randomness 53
3.4 Statistical Independence 56
3.5 Independence with Three or More Events 61
v
vj Contents
3.6 Independent versus Mutually Exclusive Events: Additional Rules 63
3.7 Introduction to Markov Processes: Nonrandom yet Acyclical 64
3.8 Randomness in Finite Sequences 66
Chapter IV Random Variables and their Distributions 72
ij Definition of a Random Variable: The Discrete Case 72
4.2 Continuous Random Variables 77
4.3 Functions of Random Variables: Transformations 80
4.4 The Uniform Transformation: Quantiles 83
4.5 Jointly Distributed Random Variables 86
4.6 Convolution and the Distribution of a Sum 89
Chapter V Expectation and Moments 99
5.1 Mathematical Expectations 99
5.2 The Expectation of a Sum 103
5.3 Expectation of a Product: Covariance 104
5.4 Moments 106
5.5 Use of Moments to Describe Distributions 108
5.6 Variance of a Sum: Extension to Higher Moments 117
5.7 Empirical Moments: Grouping 119
5.8 Estimation of Moments or other Parameters 122
Part II THE BINOMIAL PROCESS AND ITS APPLICATIONS
Chapter VI The Binomial Distribution 131
6.1 The Binomial Sequence as Model 131
6.2 The Binomial Distribution 132
6.3 Derivations 135
6.4 Binomial Tables 138
6.5 Recursion Formulas 141
6.6 The Poisson Approximation 143
6.7 Convergence of r/n on p: Bernoulli s Theorem 145
6.8 Confidence Limits forp 148
6.9 The Binomial Control Chart 154
Chapter VII The Binomial Applications of Discrimination, Acceptance 163
Sampling, and Hypothesis Testing
7.1 Introduction 163
7.2 Elements of Statistical Discrimination 164
7.3 Size of Sample in Discrimination 166
7.4 Introduction to Acceptance Sampling 168
7.5 Fraction Inspected and Outgoing Quality 172
7.6 Testing Hypotheses concerning p 174
7.7 Two Types of Error: the OC Curve 177
7.8 Acceptance and Rejection of the Null Hypothesis 180
7.9 Use of Confidence Limits in Testing Hypotheses 182
7.10 The p chart as a Test of Stability 183
7.11 Hypothesis Testing and Scien tific Inference 185
Contents vii
Chapter VIII The Lexis Process, Bayes Theorem, and Binomial Sampling 191
8.1 Introduction 191
8.2 The Lexis Process Defined 192
8.3 Mean and Variance of a Lexis Variable 195
8.4 Example of a Comparatively Nonvariable Process 197
8.5 The Lexis Process and Acceptance Sampling 199
8.6 Fraction Inspected and Outgoing Quality for Lexis Processes 200
8.7 The Lexis Process and Bayes Theorem 202
8.8 Use of Bayes Theorem in Discrimination 203
8.9 Discrimination and Maximum Likelihood 205
8.10 Bayes Theorem and the Testing of Hypotheses 206
8.11 Difficulties of Statistical Analysis 207
Chapter IX The Negative Binomial Distribution 213
9.1 Negative versus Positive Binomial 213
9.2 Two Basic Distributions: Their p.f.s and c.d.f.s 214
9.3 Moments 216
9.4 The Geometric Distribution as a Special Case: Randomness and 218
Runs
9.5 Length of Runs in a Markov Process 221
9.6 The Negative Binomial as Model 223
Chapter X The Economics of Acceptance Sampling 228
10.1 Economy in Sampling 228
10.2 The Dodge Romig Approach to Economy in Sampling 229
10.3 A Simple Linear Cost Model 229
10.4 Illustration of Minimum Cost Sampling 235
10.5 Sample Design and the Minimax Principle 238
10.6 A Brief Comment on Size of Lots 240
10.7 Limitations of the Cost Model 241
10.8 Sampling Design in Perspective 243
Part III THE POISSON PROCESS
Chapter XI The Poisson Distribution 245
11.1 The Poisson Process in Brief 245
11.2 The Poisson Process as the Limit of a Binomial 246
11.3 An Alternative Derivation of the Poisson Distribution 249
11.4 Characteristics of the Poisson Distribution 250
11.5 The Incomplete First Moment: Inventory Control 251
11.6 The Sum of Poisson Processes 254
11.7 Mixtures of Poisson Processes 255
11.8 The Poisson Control Chart and a Test for Conformity 260
11.9 Problems of Estimation 262
Chapter XII The Gamma Distribution: A Model for Analyzing Waiting Times 271
12.1 The Waiting Time for r Poisson Occurrences 271
12.2 The Gamma Distribution 273
viii Contents
12.3 The Exponential Distribution: r = 1 276
12.4 Generation of an Artificial Poisson Process 279
12.5 Percentage Points, Tests, and Confidence Limits 282
12.6 The Sum of Gamma Variables with a Common m 285
12.7 Introduction to Life Testing 286
12.8 Alternatives to the Exponential Model in Life Testing 290
*12.9 Mathematical Note I: The Gamma and Beta Functions 293
*12.10 Mathematical Note II: Sums and Ratios of Gamma Variables 296
*12.11 Mathematical Note III: Derivation of the Normal Limit 299
Part IV THE NORMAL PROCESS
Chapter XIII The Normal Distribution as an Approximation for other 305
Distributions
13.1 Convergence on the Normal: A General Tendency 305
13.2 The Central Limit Theorem 306
13.3 The Normal Distribution: Characteristics 308
13.4 Moments 311
13.5 Tables of the Normal Distribution 312
13.6 The Normal Approximation 313
13.7 The Normal Approximation to the Binomial 316
13.8 The Normal Approximation to the Hypergeometric 319
13.9 Acceptance Regions and Confidence Intervals 319
13.10 Convolution of the Rectangular Distribution 323
13.11 Normally Distributed Random Numbers 325
Chapter XIV Sampling from a Normal Process: Estimation of /x and a 330
14.1 Introduction to Normal Sampling 330
14.2 The Distribution of Sample Means: The x Chart 331
14.3 Tests and Confidence Intervals for /u with Known a 333
14.4 Unknown a and Student s t distribution 334
14.5 The Distribution of 2(Xj n)2 /a2 337
14.6 A Geometrical Interpretation of Chi Square 339
14.7 The Distribution of 2(x{ x)2 /a2 340
14.8 Inferences concerning a and a2: Problems of Estimation 342
14.9 The Variance Ratio 344
14.10 Skewness and Kurtosis in Samples 347
14.11 Quantiles and Ranges 349
14.12 Con trol Charts for x, a, and R 351
Chapter XV Normal Stable Chaos and the Analysis of Variance 360
15.1 A Brief Survey of a Large Subject 360
15.2 From x Chart to ANOVA 361
15.3 The Decomposition of Squares 363
15.4 Theory of the One way Layout 364
15.5 Departures from Ideal Conditions 369
15.6 Tests for Stability of Variance 372
15.7 Difficulties of Interpretation: Ranking of Means 373
Contents ix
15.8 Difficulties of Interpretation: Type II Errors 375
15.8a Appendix to Section 15.8: Least Squares 378
15.9 Additional Sources of Variation: the Two Way Layout 379
15.10 Beyond the Two Way Layout: Choice of Design 382
Chapter XVI A Few Normalizing Transformations 386
16.1 Use of Transformations 386
16.2 The Square root Transformation 387
16.3 The Inverse Sine Transformation for Proportions 388
16.4 A Polynomial Correction for Skewness 389
16.5 The Logarithmic Transformation 391
16.6 Powers, Products, Ratios, and Roots 395
16.7 A Generalized Logarithmic Transformation 396
16.8 Johnson s Generalized Transformations 398
Part V PROCESS VERSUS MODEL
Chapter XVII Model versus Process in General 403
17.1 What is a Frequency Model 403
17.2 Selection of Models: Systematic Approaches 404
17.3 Testing of Models: An Introduction 407
17.4 Two Motives for Testing Models 408
17.5 The Question of Sample Size 410
17.6 Multiple Tests and their Interpretation 410
17.7 Retrospective Testing 412
17.8 The Role of Judgment 414
Chapter XVIII Pearson s System of Frequency Models 417
18.1 The Pearson System in Brief 417
18.2 Moments, Skewness, and Kurtosis 418
18.3 Solutions to Pearson s Differential Equation 419
18.4 Identification of Types 422
18.5 The Type I Distributions 425
18.6 The Type VI Distribution 427
18.7 The Type III Distribution 429
18.8 The Type VDistribution 429
18.9 Types IVand VII 430
18.10 Evaluation of Parameters 432
18.11 Two Examples of Fitting Pearson Curves to Data 433
18.12 Mathematical Note: Likelihood Estimation for Type III 441
Chapter XIX The Kolmogorov Smirnov Test 446
19.1 The Kolmogorov Smirnov Test in General 446
19.2 Illustration of the Basic One Sample Test 447
19.3 The Limiting Distribution of Dn 450
19.4 A Confidence Region for F(x) 451
19.5 Sensitivity of the One Sample Test: A Simple Improvement 452
19.6 Use of Grouped Data 453
x Contents
19.7 Linearization of Fq(x) 456
19.8 The Two Sample Test and Its Generalization 459
Chapter XX The Chi square Test: Goodness of Fit 464
20.1 A General Purpose Test 464
20.2 The Basic Chi square Test 465
20.3 The Relation between X2 and x2 : Degrees of Freedom 468
20.4 Problems of Grouping 470
20.5 Estimation of Unspecified Parameters 470
20.6 Type II Errors and Sample Size 473
20.7 Goodness of Fit: Difficulties of Measurement 475
20.8 Chi square and Continuous Distributions 478
Chapter XXI The Chi square Test: Contingency Tables 483
21.1 Independence in Contingency Tables 483
21.2 Special Treatments for 2 x 2 Tables 488
21.3 The 2xc Table for Testing Binomial Stability 491
21.4 Measurement of Association 494
21.5 Testing for Serial Independence 495
21.6 Chi square and Stable Chaos 496
21.7 Epilogue 499
APPENDICES
Appendix A Glossary of Notation 505
Appendix B Tables 511
B l The Binomial Distribution Function 512
B 2 Charts Providing Confidence Limits for the Binomial Parameter p 515
B 3 Cumulative Poisson, Chi square, and Gamma Distributions 519
B 4 Critical Quantiles of the Gamma Distribution 527
B 5 Common Logarithms of the Generalized Factorial 529
B 6 The Standarized Normal Probability Functions 530
B 7 Quantiles of the Standarized Normal Distribution 531
B 8 Means and Standard Deviations of a la, s/o. and R/o 532
B 9 Critical Values for the Kolmogorov Smimov Test 533
B 10Kolmogorov s Limit for the Distribution of the Maximum
Absolute Difference 534
B l 1 Noncentral Chi square: Values of 8 2 for 0, a 536
B l2 Ten Thousand Pseudorandom Digits 537
B 13Nearly Normal Random Numbers: n = 6, a = 1 544
ANSWERS TO EXERCISES 553
BIBLIOGRAPHY AND AUTHOR INDEX 561
SUBJECT INDEX 573
|
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| spelling | Durand, David Verfasser aut Stable chaos An introd. to statistical control Morristown, N.J. General Learning Pr. 1971 XV,582 S. txt rdacontent n rdamedia nc rdacarrier D.H.Mark publication. Statistik (DE-588)4056995-0 gnd rswk-swf Statistik (DE-588)4056995-0 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001949231&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Durand, David Stable chaos An introd. to statistical control Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4056995-0 |
| title | Stable chaos An introd. to statistical control |
| title_auth | Stable chaos An introd. to statistical control |
| title_exact_search | Stable chaos An introd. to statistical control |
| title_full | Stable chaos An introd. to statistical control |
| title_fullStr | Stable chaos An introd. to statistical control |
| title_full_unstemmed | Stable chaos An introd. to statistical control |
| title_short | Stable chaos |
| title_sort | stable chaos an introd to statistical control |
| title_sub | An introd. to statistical control |
| topic | Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistik |
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