Statistical theory with engineering applications:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English Danish |
| Veröffentlicht: |
New York [u.a.]
Wiley
1967
|
| Ausgabe: | 7. print. |
| Schriftenreihe: | A Wiley publication in applied statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 783 S. |
| ISBN: | 0471340561 |
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| 245 | 1 | 0 | |a Statistical theory with engineering applications |c A. Hald |
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Datensatz im Suchindex
| _version_ | 1810082162597167104 |
|---|---|
| adam_text |
Contents
1 Fundamental Calculus of Probabilities 1
1.1 The Concept of Probability 1
1.2 Some Fundamental Properties of Frequencies 4
1.8 Definitions and Axioms of the Calculus of Probabilities 9
1.4 The Addition Formula 11
1.5 The Multiplication Formula 15
1.6 Stochastic and Causal Dependence 19
1.7 Notes and References 21
2 Some Fundamental Applications op the Calculus of Probabilities 23
2.1 The Binomial Distribution 23
2.2 The Multinomial Distribution 36
2.3 Pascal's Distribution 38
2.4 The Hypergeometric Distribution 40
3 Graphical and Tabular Representation of Observations 44
Empirical Distribution of a Single Continuous Variable 44
3.1 Dot Diagram and Enumeration 44
3.2 Tabulation and Grouping 46
3.3 The Histogram and the Frequency Polygon 49
3.4 The Length of the Class Interval 51
3.5 The Cumulative Frequency Polygon 53
Empirical Distribution of a Single Discontinuous Variable 55
3.6 Enumeration and Graphical Representation 55
Multi-Dimensional Distributions 57
3.7 Dot Diagram 57
3.8 Punched Cards 58
3.9 Tables and Histograms 62
4 Definitions and Fundamental Properties of Empirical Distributions 66
4.1 Statement of the Problem 66
4.2 Fractiles 66
4.3 Definition and Computation of the Mean 67
4.4 Definition and Computation of the Variance 72
4.5 The Normal Distribution 77
4.6 Marginal Means and Variances 80
4.7 Conditional Means and Variances 81
4.8 Definition and Computation of the Covariance 85
5 Definitions and Fundamental Properties of Theoretical Distributions . 90
One-Dimensional Distributions 90
5.1 The Cumulative Distribution Function 90
5.2 Continuous Distributions 91
5.3 Discontinuous Distributions 95
vii
viii CONTENTS
5.4 The Concept of a Population 97
5.5 Transformation of Distributions 99
5.6 Fractiles 102
5.7 The Mean of a Stochastic Variable 103
5.8 The Mean of a Function of a Stochastic Variable 105
5.9 The Variance of a Stochastic Variable 106
5.10 Tchebycheff's Theorem 109
Two-Dimensional Distributions 110
5.11 The Cumulative Distribution Function 110
5.12 Continuous Distributions Ill
5.13 Discontinuous Distributions 113
5.14 Marginal Means and Variances 114
5.15 Conditional Means and Variances 114
5.16 The Covariance 115
5.17 The Mean and Variance of a Linear Function of Stochastic Variables 117
6 The Normal Distribution 119
6.1 Definitions 119
6.2 The Parameters of the Distribution 120
6.3 The Standardized Normal Distribution. The u-Distribution 121
6.4 The Distribution Function 124
6.5 The Cumulative Distribution Function 125
6.6 The Fractiles 127
6.7 The Fractile Diagram 130
6.8 Fitting a Normal Distribution to Observed Data 140
6.9 The Truncated Normal Distribution 144
6.10 Heterogeneous Distributions 152
7 Skew Distributions 159
7.1 Transformation of Skew Distributions 159
7.2 The Logarithmic Normal Distribution 160
7.3 Other Transformations 174
7.4 Notes and References 185
7.5 Summary 187
8 Some Limit Theorems and Sampling Distributions 188
8.1 Introduction 188
8.2 The Central Limit Theorem 188
8.3 Kapteyn's Derivation of Skew Distributions 195
8.4 The Concept of a Sampling Distribution 197
8.5 The Sampling Distribution of the Mean 199
8.6 The Sampling Distribution of the Variance 202
8.7 The Law of Large Numbers 203
8.8 The Method of Maximum Likelihood 204
8.9 Unbiased and Sufficient Estimates 208
8.10 Stochastic Dependence and Independence 210
9 The Distribution of the Mean 214
9.1 The Addition Theorem for the Normal Distribution 214
9.2 The Distribution of the Mean 219
9.3 The Fractiles 221
9.4 The u-Test of Significance 224
9.5 Confidence Limits for £ 239
9.6 Summary 242
CONTENTS ix
9.7 The Weighted Mean 243
9.8 The Distribution of the Estimate of the Parameter f in a Truncated Normal Dis¬
tribution 245
9.9 An Approximate Formula for the Mean and Variance of Indirect Observations . '246
9.10 Notes and References 251
10 The x2-Disteibution 253
10.1 Statement of the Problem 253
10.2 The Distribution Function of x2 254
10.3 The Cumulative Distribution Function and the Fractiles 256
10.4 Derivation of the x2-Distribution 258
10.5 The Addition Theorem for the ^-Distribution 261
10.6 The Partition Theorem for the x2-Distribution 262
10.7 Notes and References 274
11 The Distribution of the Variance 276
11.1 The Distribution of the Variance 276
11.2 The Fractiles 278
11.3 The x2-Test of Significance 280
11.4 Confidence Limits for a2 286
11.5 The Addition Theorem for the ^-Distribution 287
11.6 A Test for the Equality of k Theoretical Variances 290
11.7 The Distribution of the Standard Deviation 299
11.8 The Distribution of the Coefficient of Variation 301
11.9 The Control of Proportion Defective by Means of a Linear Function of x and s . 303
11.10 Tolerance Limits 311
11.11 The Distribution of the Estimate of r in a Truncated Normal Distribution . 316
12 The Distribution of the Range 319
12.1 The Distribution Function of the Range 319
12.2 The Control Chart for the Range 322
12.3 Confidence Limits for r 326
13.4 The Distribution of the Largest Observation 329
12.5 The Distribution of the Largest Deviation from the Population Mean 331
12.6 The Studentized Range 332
12.7 Largest Observation Minus Sample Mean 332
12.8 Criteria for Rejection of Outlying Observations 333
12.9 References 336
13 Statistical Control 338
13.1 Introduction 338
13.2 The State of Statistical Control. Randomness 338
13.3 Runs above and below the Median 342
13.4 Runs up and down 353
13.5 The Mean Square Successive Difference 357
13.6 Detecting Lack of Control in Respect to a Specified Distribution 360
13.7 Detecting Lack of Control When the Distribution is Unknown 363
13.8 The State of Maximum Control 369
13.9 Specification Limits and Statistical Control 370
13.10 Notes and References 371
14 The Distribution op the Variance Ratio 374
14.1 The ^-Distribution 374
14.2 The t^-Test of Significance 379
X CONTENTS
14.3 Confidence Limits for r\/a\ 381
14.4 Derivation of the ^-Distribution 381
14.5 Special Cases of the ^-Distribution 384
15 The ^-Distribution 388
15.1 The f-Distribution 388
15.2 The i-Test of Significance 391
15.3 Confidence Limits for £ 394
15.4 Comparison of Two Sets of Stochastically Independent Observations 394
15.5 Comparison of the Effects of Two Treatments 401
15.6 Combination of Tests of Significance 407
15.7 Comparison of Two Truncated Distributions 410
15.8 References 410
16 Analysis of Variance 412
16.1 Analysis of Variance and the i-Test 412
16.2 Two Types of Problem Dealt with by Means of Analysis of Variance 417
16.3 Partitioning the Total Sum of Squares 419
16.4 A Test for the Equality of the Means of h Normal Populations with the Same
Variance 423
16.5 Analysis of the Variance into Two Components Representing Different Sources of
Random Variation 437
16.6 Multi-Stage Grouping 447
16.7 Two-Way Classification 456
16.8 Three-Way Classification 480
16.9 Miscellaneous Remarks .' 486
16.10 Notes and References 486
17 Designs op Sampling Investigations and Experiments 488
17.1 Introduction 488
17.2 Random Sampling from a Finite Population 488
17.3 Stratified Random Sampling 491
17.4 Two-Stage Sampling 496
17.5 The Ratio Estimate 498
17.6 Experiments and Statistical Control. Randomization 500
17.7 Randomized Blocks 504
17.8 Latin Squares 507
17.9 Systematic Arrangements 510
17.10 Factorial Experiments 513
17.11 Notes and References 520
18 Linear Regression Analysis with One Independent Variable 522
18.1 Introduction 522
18.2 Hypotheses Underlying Regression Analysis 526
18.3 Derivation of the Estimates of the Parameters 528
18.4 Tests of Significance. Confidence Limits 540
18.5 Solving the Regression Equation with Respect to the Independent Variable . . 549
18.6 The Variance is Proportional to a Given Function of the Independent Variable . 551
18.7 Transforming the Regression Curve to a Straight Line 558
18.8 Comparison of Two Regression Lines 571
18.9 Comparison of Several Regression Lines 579
18.10 Markoff's Theorem 584
CONTENTS XI
19 The Two-Dimensional Normal Distribution 585
19.1 Correlation and Regression 585
19.2 The Distribution Function 585
19.3 The Standardized Distribution 588
19.4 The Marginal Distributions 590
19.5 The Correlation Coefficient and the Covariance 591
19.6 The Estimates of the Parameters 592
19.7 The Conditional Distributions 593
19.8 Linear Transformations of the Variables 596
19.9 The Contour Ellipses 599
19.10 Examination of an Observed Two-Dimensional Distribution 602
19.11 Distribution of the Means. Confidence Regions. Tests of Significance . 606
19.12 The Distribution of the Correlation Coefficient 608
19.13 The Interpretation of the Correlation Coefficient 613
19.14 The Influence of Errors of Measurement on the Correlation and Regression Coef¬
ficients 615
19.15 Tests of Significance for the Regression Coefficients 616
19.16 Comparison of Two Sets of Two-Dimensional Observations 616
19.17 Remarks on Some Models of Two-Dimensional Relationships 621
20 Multi-Dimensional Correlation and Regression 624
20.1 Partial Correlation Coefficients 624
20.2 Linear Regression Analysis with Two Independent Variables 627
20.3 Linear Regression Analysis with m Independent Variables 638
20.4 Non-Linear Regression with One Independent Variable 649
20.5 Non-Linear Regression with m Independent Variables 656
20.6 Regression Analysis and the Analysis of Variance 657
20.7 Growth Curves 658
20.8 Time Series 662
20.9 Literature on Regression, Correlation and Related Subjects 665
21 The Binomial Distribution 668
21.1 The Distribution Function 668
21.2 The Cumulative Distribution Function and the Fractiles 672
21.3 The Binomial Distribution and the i^-Distribution 674
21.4 The Mean and the Variance 675
21.5 The Binomial Distribution and the Normal Distribution 676
21.6 The Transformation 2 arcsin -\/h 685
21.7 The Binomial Distribution and the PoissoN-Distribution 688
21.8 The Binomial Distribution and the Hypergeometric Distribution 690
21.9 The Control Chart for Proportion Defective 692
21.10 Comparing an Observed Frequency with a Hypothetical Probability 694
21.11 Confidence Limits 697
21.12 Sampling Inspection by Attributes 700
21.13 Comparison of Two Frequencies 705
21.14 Comparison of A; Frequencies 711
22 The Poisson Distribution 714
22.1 The Distribution Function and the Cumulative Distribution Function 714
22.2 The PoissON-Distribution and the Normal Distribution 717
22.3 The Control Charts for the Number of Defectives and Defects 718
22.4 A Test of Significance for the Difference between an Observed and an Expected
Number 721
22.5 Confidence Limits 722
Xli CONTENTS
22.6 The Addition Theorem for the Poissox-Distribution 724
22.7 Comparison of Two PoissoN-Distributed Observations 725
22.8 Comparison of k Poissox-Distributed Observations 726
24.9 The Compound PoissoN-Distribution 727
22.10 Discontinuous Stochastic Processes 731
22.11 Statistical Equilibrium 736
23 The Multinomial Distribution and the x2-Test 739
23.1 The Multinomial Distribution and the ^-Distribution 739
23.2 Comparison of an Observed Grouped Distribution and a Theoretical Distribution 742
23.3 A Test of Stochastical Independence 744
23.4 Comparison of k Observed Grouped Distributions 746
24 Sequential Analysis 749
24.1 Some Principles of Sequential Tests 749
24.2 Some Special Cases of Sequential Tests 754
25 The Main Points of a Statistical Analysis 756
25.1 Formulation of the Problem 756
25.2 The Sampling Method and the Number of Observations 757
25.3 The Specification 758
25.4 Estimating the Parameters 759
25.5 Investigation of the Agreement between the Model and the Observations . 759
25.6 Tests of Significance 760
Notation 761
List of Author References 763
Index of Symbols and Formulas 767
Index of Subjects 773 |
| any_adam_object | 1 |
| author | Hald, Anders 1913-2007 |
| author_GND | (DE-588)1126043001 |
| author_facet | Hald, Anders 1913-2007 |
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| author_variant | a h ah |
| building | Verbundindex |
| bvnumber | BV001929021 |
| classification_rvk | QH 232 SK 850 |
| ctrlnum | (OCoLC)257982523 (DE-599)BVBBV001929021 |
| dewey-full | 519.522 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.522 |
| dewey-search | 519.522 |
| dewey-sort | 3519.522 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 7. print. |
| format | Book |
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| genre | Statistik |
| genre_facet | Statistik |
| id | DE-604.BV001929021 |
| illustrated | Not Illustrated |
| indexdate | 2024-09-13T12:01:08Z |
| institution | BVB |
| isbn | 0471340561 |
| language | English Danish |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001257248 |
| oclc_num | 257982523 |
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| physical | XII, 783 S. |
| psigel | TUB-www |
| publishDate | 1967 |
| publishDateSearch | 1967 |
| publishDateSort | 1967 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley publication in applied statistics |
| spelling | Hald, Anders 1913-2007 Verfasser (DE-588)1126043001 aut Statistiske metoder, med eksempler paa anvendelser indenfor teknikken Statistical theory with engineering applications A. Hald 7. print. New York [u.a.] Wiley 1967 XII, 783 S. txt rdacontent n rdamedia nc rdacarrier A Wiley publication in applied statistics Wahrscheinlichkeitstheorie Ingenieurwissenschaften (DE-588)4137304-2 gnd rswk-swf Theorie (DE-588)4059787-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Statistik Statistik (DE-588)4056995-0 s Theorie (DE-588)4059787-8 s DE-604 Ingenieurwissenschaften (DE-588)4137304-2 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001257248&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hald, Anders 1913-2007 Statistical theory with engineering applications Wahrscheinlichkeitstheorie Ingenieurwissenschaften (DE-588)4137304-2 gnd Theorie (DE-588)4059787-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4137304-2 (DE-588)4059787-8 (DE-588)4056995-0 |
| title | Statistical theory with engineering applications |
| title_alt | Statistiske metoder, med eksempler paa anvendelser indenfor teknikken |
| title_auth | Statistical theory with engineering applications |
| title_exact_search | Statistical theory with engineering applications |
| title_full | Statistical theory with engineering applications A. Hald |
| title_fullStr | Statistical theory with engineering applications A. Hald |
| title_full_unstemmed | Statistical theory with engineering applications A. Hald |
| title_short | Statistical theory with engineering applications |
| title_sort | statistical theory with engineering applications |
| topic | Wahrscheinlichkeitstheorie Ingenieurwissenschaften (DE-588)4137304-2 gnd Theorie (DE-588)4059787-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitstheorie Ingenieurwissenschaften Theorie Statistik |
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