Probability and statistical inference for scientists and engineers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Englewood Cliffs, NJ [u.a.]
Prentice-Hall
1973
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 596 S. graph. Darst. |
| ISBN: | 0137116225 |
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MARC
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| 100 | 1 | |a Gibra, Isaac N. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Probability and statistical inference for scientists and engineers |c Isaac N. Gibra |
| 264 | 1 | |a Englewood Cliffs, NJ [u.a.] |b Prentice-Hall |c 1973 | |
| 300 | |a XII, 596 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Ingénierie - Méthodes statistiques | |
| 650 | 4 | |a Probabilités | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Engineering |x Statistical methods | |
| 650 | 4 | |a Probabilities | |
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Record in the Search Index
| _version_ | 1804132829116760064 |
|---|---|
| adam_text | CONTENTS
PREFACE xi
Part I
PROBABILITY
Chapter I ELEMENTS OF PROBABILITY THEORY 3
1.1 Historical Introduction to Probability Theory 3
1.2 Some Basic Notions of Set Theory 4
1.3 Sample Space 7
1.4 Fundamental Probability Theorems 9
1.5 Combinatorial Analysis 19
Chapter 2 PROBABILITY FUNCTIONS 30
2.1 Random Variables 30
2.2 Distribution Functions 32
2.3 Probability Functions 34
2.4 Density Functions 35
2.5 Empirical Frequency Distributions 39
2.6 The Monte Carlo Technique 43
v
vi Contents
Chapter 3 JOINT DISTRIBUTION FUNCTIONS 55
3.1 Basic Concepts 55
3.2 Joint Distribution Functions 56
3.3 Joint Probability Functions 59
3.4 Joint Density Functions 65
Chapter 4 DISTRIBUTIONS OF FUNCTIONS OF RANDOM VARIABLES 77
4.1 Introduction 77
4.2 Function of a Single Variate 78
4.3 The Distribution of a Function of Two or More Variates 85
4.4 Joint Distributions of Functions of Random Variables 89
Chapter 5 EXPECTATION 100
5.1 Measures of Location 100 [
5.2 Properties of the Mean 104
5.3 Conditional Expectation 105
5.4 Measures of Variation 107
5.5 Properties of the Variance 109
5.6 Covariance and Correlation 111
5.7 Chebyshev s Inequality 116
5.8 The Law of Large Numbers 117
5.9 Moment Generating Function 118
5.10 The Central Limit Theorem 123 I
(
Chapter 6 SOME IMPORTANT DISTRIBUTIONS 133
6.1 Introduction 133
6.2 Binomial Distribution 133
6.3 Poisson Distribution 137
6.4 Multinomial Distribution 140
6.5 Hypergeometric Distribution 142
6.6 Geometric Distribution 144
6.7 Negative Binomial 145
6.8 Normal Distribution 148
6.9 Bivariate Normal Distribution 152
6.10 Log Normal Distribution 154
6.11 Exponential Distribution 155
6.12 Uniform Distribution 157
6.13 Gamma Distribution 158
6.14 Chi square Distribution 160
6.15 Student s t Distribution 162
6.16F Distribution 163
6.17 Weibull Distribution 166
6.18 The Beta Distribution 168 r
6.19 Approximations 170
Part II
STATISTICAL INFERENCE AND APPLICATIONS
Chapter 7 ORDER STATISTICS 185
7.1 Introduction 185
7.2 Distribution of the Largest Element in a Sample 186
7.3 Distribution of the Smallest Element in a Sample 187
7.4 Distribution of the Median of a Sample 188
7.5 Distribution of the /th Order Statistic of a Sample 190
7.6 Distribution of the Range of a Sample 191
7.7 Distribution Free Tolerance Limits 193
Chapter 8 SIGNIFICANCE TESTS 201
8.1 Introduction 201
8.2 Introductory Example 201
8.3 Statistical Decision Theory 202
8.4 Kinds of Tests 211
Chapter 9 STATISTICAL HYPOTHESES TESTING {Single Parameter) 213
9.1 The Likelihood Function 213
9.2 Neyman Pearson Lemma 214
9.3 Likelihood Ratio Tests of Composite Hypotheses 216
9.4 Tests Concerning the Mean of a Normal Distribution (/i) with
Known Variance O§) 217
9.5 Tests Concerning the Mean of a Normal Distribution (ft) with Un¬
known Variance (a1) 227
9.6 Tests Concerning the Variance of a Normal Distribution 233
9.7 Tests Concerning the Parameters of Distributions Other Than the
Normal 237
Chapter 10 STATISTICAL HYPOTHESES TESTING (Two Parameters) 250
10.1 Tests Concerning the Difference of Means of Two Independent
Normal Distributions with Known Variances 250
10.2 Tests Concerning the Difference of Means of Two Independent
Normal Distributions with Equal but Unknown Variances 256
10.3 Tests Concerning the Difference of Means of Two Independent
Normal Distributions with Unknown and Unequal Variances 259
10.4 Tests Concerning the Equality of Variances of Two Independent
Normal Distributions 261
10.5 Test Concerning the Equality of Variances of Several Independent
Normal Distributions 263
vii
viii Contents
10.6 Paired Comparisons 265
10.7 Comparison of Two Binomial Populations 269
Chapter II NONPARAMETRIC TESTS 282
11.1 Introduction 282
11.2 The Sign Test 283
11.3 The Wilcoxon Two Sample Rank Test 287
11.4 The//Test 293
11.5 Run Tests 295
11.6 Bivariate Techniques 300
Chapter 12 ESTIMATION 309
12.1 Introduction 309
12.2 Point Estimation 309
12.3 Interval Estimation 322
12.4 Confidence Limits for the Parameter p of the Binomial Distribu¬
tion 328
Chapter 13 ANALYSIS OF VARIANCE 337
13.1 Introduction 337
13.2 One Way Classification; Fixed Effects Model 338
13.3 One Way Classification; Random Effects Model 365
13.4 Two Way Classification; Fixed Effects Model; One Observation
per Cell 371
13.5 Two Way Classification; Random Effects Model; One Observa¬
tion per Cell 378
13.6 Two Way Classification; Mixed Effects Model; One Observation
per Cell 381
13.7 Computing Formulas and Procedure; One Observation per Cell 382
13.8 Two Way Classification; Fixed Effects Model; n Observations
per Cell 385
13.9 Two Way Classification; Random Effects Model; n Observations
per Cell 392
13.10 Two Way Classification; Mixed Effects Model; n Observations
per cell 394
13.11 Computing Formula and Procedure; n Observations per Cell 395
13.12 Concluding Remarks 398
Chapter 14 LINEAR REGRESSION AND CORRELATION 408
14.1 Introduction to Regression Analysis 408
14.2 Simple Linear Regression 411
14.3 Multiple Regression 433 :
14.4 Linear Correlation 435
Contents ix
Chapter IS GOODNESS OF FIT TESTS 449
15.1 Introduction 449
15.2 The x2 Test 450
15.3 Contingency Tables (Two by Two Case) 454
15.4 Contingency Tables (r X s case) 458
15.5 The Kolmogorov Smirnov Tests 459
Chapter 16 CONTROL CHARTS 466
16.1 Statistical Stability 466
16.2 Control Chart for the Mean: X Chart 467
16.3 Control Chart for the Range: R Chart 473
16.4 Control Chart for the Standard Deviation: a Chart 474
16.5 Starting the Control Charts 475
16.6 The Role of Normality in Sampling Theory 478
16.7 Natural Tolerance Limits 479
16.8 Control Chart for Fraction Defective: p Chart 480
16.9 Control Chart for the Number of Defects in a Sample: np Chart 483
16.10 Control Chart for Defects: c Chart 483
Chapter 17 ACCEPTANCE SAMPLING 490
17.1 Introduction 490
17.2 Single Sampling Plans 491
17.3 Average Outgoing Quality 498
17.4 Double Sampling Plans 500
17.5 Sequential Sampling Plans 504
17.6 Other Types of Attributes Plans 508
17.7 Introduction 509
17.8 Single Sampling Plans by Variables—Sigma Known and Constant 510
17.9 Sequential Sampling Plans by Variables—Sigma Known and Constant 513
Chapter 18 SOME ASPECTS OF QUEUBNG THEORY 520
18.1 Introduction 520
18.2 Basic Elements of Queueing Systems 521
18.3 The State of the System 524
18.4 Terminology and Notation 526
18.5 Single Channel, Infinite, Poisson Arrival, Exponential Service
Queues 527
18.6 Single Channel, Infinite, Poisson Arrival, Nonexponential
Service Queues 533
18.7 Single Channel, Finite, Poisson Arrival, Exponential Service
Queues 534
18.8 Multichannel, Finite, Poisson Arrival, Exponential Service Queues 538
18.9 Multichannel, Infinite, Poisson Arrival, Exponential Service Queues 542
18.10 Simulation of Queues 545
x Contents
APPENDIX TABLES 550
A Random Digits 551
B Powers and Roots 555
C Values of e~* 557
D The Cumulative Standardized Normal Distribution Function 560
E Ordinates of the Normal Density Function 562
F The ^ Distribution 563
G The ^ Distribution 564
H The F Distribution 566
I The Poisson Distribution Function 572
J The Binomial Distribution Function 577
K Distribution of the Studentized Range 582
L Factors for Computing Control Chart Lines 584
ANSWERS 585
INDEX 592
|
| any_adam_object | 1 |
| author | Gibra, Isaac N. |
| author_facet | Gibra, Isaac N. |
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| dewey-ones | 519 - Probabilities and applied mathematics |
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| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV019383876 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:59:02Z |
| institution | BVB |
| isbn | 0137116225 |
| language | English |
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| physical | XII, 596 S. graph. Darst. |
| psigel | TUB-nveb |
| publishDate | 1973 |
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| publisher | Prentice-Hall |
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| spelling | Gibra, Isaac N. Verfasser aut Probability and statistical inference for scientists and engineers Isaac N. Gibra Englewood Cliffs, NJ [u.a.] Prentice-Hall 1973 XII, 596 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Ingénierie - Méthodes statistiques Probabilités Ingenieurwissenschaften Engineering Statistical methods Probabilities HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012846839&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gibra, Isaac N. Probability and statistical inference for scientists and engineers Ingénierie - Méthodes statistiques Probabilités Ingenieurwissenschaften Engineering Statistical methods Probabilities |
| title | Probability and statistical inference for scientists and engineers |
| title_auth | Probability and statistical inference for scientists and engineers |
| title_exact_search | Probability and statistical inference for scientists and engineers |
| title_full | Probability and statistical inference for scientists and engineers Isaac N. Gibra |
| title_fullStr | Probability and statistical inference for scientists and engineers Isaac N. Gibra |
| title_full_unstemmed | Probability and statistical inference for scientists and engineers Isaac N. Gibra |
| title_short | Probability and statistical inference for scientists and engineers |
| title_sort | probability and statistical inference for scientists and engineers |
| topic | Ingénierie - Méthodes statistiques Probabilités Ingenieurwissenschaften Engineering Statistical methods Probabilities |
| topic_facet | Ingénierie - Méthodes statistiques Probabilités Ingenieurwissenschaften Engineering Statistical methods Probabilities |
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