Mathematical statistics with applications:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boston, Mass.
Duxbury Pr.
1986
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| Edition: | 3. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 750 S. graph. Darst. |
| ISBN: | 0871509393 |
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| 245 | 1 | 0 | |a Mathematical statistics with applications |c William Mendenhall ; Richard L. Scheaffer ; Dennis D. Wackerly |
| 250 | |a 3. ed. | ||
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Record in the Search Index
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| adam_text | Titel: Mathematical statistics with applications
Autor: Mendenhall, William
Jahr: 1986
Contents Preface V Note to the Student viii what Is Statistics? - 1 1.1 Introduction 1 1.2 Characterizing a Set of Measurements: Graphical Methods 3 1.3 Characterizing a Set of Measurements: Numerical Methods 7 1.4 How Inferences Are Made 11 1.5 Theory and Reality 12 1.6 Summary 13 Probability — ---- 17 2.1 Introduction 17 2.2 Probability and Inference 18 2.3 A Review of Set Notation 20 2.4 A Probabilistic Model for an Experiment: The Discrete Case 23 2.5 Calculating the Probability of an Event: The Sample-Point Method 31 2.6 Tools for Use When Counting Sample Points 35 2.7 Conditional Probability and the Independence of Events 45 2.8 Two Laws of Probability 50 2.9 Calculating the Probability of an Event: The Event-Composition Method 53 2.10 Bayes’s Rule 61 2.11 Numerical Events and Random Variables 63 2.12 Random Sampling 65 2.13 Summary 67
X Contents Discrete Random Variables and Their Probability Distributions - — - --------------------- 73 3.1 Basic Definition 73 3.2 The Probability Distribution for a Discrete Random Variable 74 3.3 The Binomial Probability Distribution 78 3.4 The Geometric Probability Distribution 86 3.5 The Hypergeometric Probability Distribution 89 3.6 The Poisson Probability Distribution 92 3.7 The Expected Value of a Random Variable or a Function of a Random Variable 97 3.8 Some Techniques Useful in Finding Expected Values for Discrete Random Variables 106 3.9 Moments and Moment-generating Functions __ 110 3.10 Probability-generating Functions (Optional) 115 3.11 Tchebysheff’s Theorem 118 3.12 Summary 121 Continuous Random Variables and Their Probability Distributions .. _ _ . ? ___ — - - 127 4.1 Introduction 127 4.2 The Probability Distribution for a Continuous Random Variable 128 4.3 The Uniform Distribution 138 4.4 The Normal Distribution 140 4.5 The Gamma-Type Probability Distribution 144 4.6 The Beta Probability Distribution 148 4.7 Some General Comments 151 4.8 The Expected Value for a Continuous Random Variable 152 4.9 Other Expected Values 157 4.10 Tchebysheff’s Theorem 162 4.11 Expectations of Discontinuous Functions and Mixed Probability Distributions (Optional) 165 4.12 Summary 169 Multivariate Probability Distributions --- - - - ? ? — 175 5.1 Introduction 175 5.2 Bivariate and Multivariate Probability Distributions 176
5.3 Marginal and Conditional Probability Distributions 186 5.4 Independent Random Variables 194 5.5 The Expected Value of a Function of Random Variables 199 5.6 Special Theorems 202 5.7 The Covariance of Two Random Variables 205 5.8 The Expected Value and Variance of Linear Functions of Random Variables 210 5.9 The Multinomial Probability Distribution 217 5.10 The Bivariate Normal Distribution (Optional) 221 5.11 Conditional Expectations 222 5.12 Summary 225 Functions of Random Variables 229 6.1 Introduction 229 6.2 Finding the Probability Distribution of a Function of Random Variables 230 6.3 Method of Distribution Functions 231 6.4 Method of Transformations 243 6.5 Method of Moment-generating Functions 250 6.6 Order Statistics 256 6.7 Summary 261 Sampling Distributions and the Central Limit Theorem -------------------------------- ?? - 265 7.1 Introduction 265 7.2 Sampling Distributions Related to the Normal Distribution 266 7.3 The Central Limit Theorem 279 7.4 A Proof of the Central Limit Theorem (Optional) 285 7.5 The Normal Approximation to the Binomial Distribution 287 7.6 Summary 291 Estimation ------------------- - 297 8.1 Introduction 297 8.2 Some Properties of Point Estimators 299 8.3 Some Common Unbiased Point Estimators 303 8.4 Evaluating the Goodness of a Point Estimator 306 8.5 Confidence Intervals 312 8.6 Large-Sample Confidence Intervals 317 8.7 Selecting the Sample Size 326
Contents 8.8 Small-Sample Confidence Intervals for ¡i and ^ - /¿ 2 330 8.9 A Confidence Interval for a 2 337 8.10 Summary 339 9 Properties of Point Estimators and Methods of Estimation ~ 1 ~ 345 9.1 Introduction 9.2 Relative Efficiency 9.3 Consistency 9.4 Sufficiency 9.5 Minimal Sufficiency and Minimum-Variance Unbiased Estimation 9.6 The Method of Moments 9.7 The Method of Maximum Likelihood 9.8 Summary Hypothesis Testing - 345 346 349 356 360 367 371 377 381 10.1 Introduction 10.2 Elements of a Statistical Test 10.3 Common Large-Sample Tests 10.4 Calculating Type-ll-Error Probabilities and Finding the Sample Size fortheZTest 10.5 Another Way to Report the Results of a Statistical Test: Attained Significance Levels orp-Values 10.6 Some Comments on the Theory of Hypothesis Testing 10.7 Two Tests Based on Statistics that Possess a Student’s t Distribution 10.8 Testing Hypotheses Concerning Variances 10.9 Power of Tests: The Neyman-Pearson Lemma 10.10 Likelihood Ratio Tests 10.11 Summary Linear Models and Estimation by Least Squares 381 382 388 395 399 403 405 412 420 428 434 439 11.1 Introduction 439 11.2 Linear Statistical Models 441 11.3 The Method of Least Squares 443 11.4 Fitting the Linear Model by Using Matrices 448 11.5 Properties of the Least Squares Estimators for the Model Y = 0Q + j8ix + e 454
Contents XIII 11.6 Properties of the Least Squares Estimators for the Multiple Linear Regression Model 462 11.7 Inferences Concerning the Parameters (3, 463 11.8 Inferences Concerning Linear Functions of the Model Parameters 469 11.9 Predicting a Particular Value of Y 474 11.10 A Test Statistic to Test H 0 : + 1 = j3 s + 2 = ... = /3* = 0 478 11.11 Correlation 483 11.12 Some Practical Examples 487 11.13 Summary 497 Considerations in Designing Experiments 503 12.1 The Elements Affecting the Information in a Sample 503 12.2 The Physical Process of Designing an Experiment 504 12.3 Random Sampling and the Completely Randomized Design 507 12.4 Volume-increasing Experimental Designs 510 12.5 Noise-reducing Experimental Designs 515 12.6 Summary 524 The Analysis of Variance - 527 13.1 Introduction 527 13.2 The Analysis of Variance Procedure 528 13.3 Comparison of More Than Two Means: Analysis of Variance for the Completely Randomized Design 533 13.4 Proof of Additivity of the Sums of Squares and E(MST) for a Completely Randomized Design (Optional) 537 13.5 An Analysis of Variance Table for a Completely Randomized Design 540 13.6 Estimation in the Completely Randomized Design 545 13.7 The Analysis of Variance for a Randomized Block Design 548 13.8 Estimation in the Randomized Block Design 555 13.9 Selecting the Sample Size 556 13.10 Simultaneous Confidence Intervals for More Than One Parameter 559 13.11 Analysis of Variance Using Linear Models 561 13.12 Summary 566
xiv Contents Analysis of Enumerative Data 573 14.1 A Description of the Experiment 14.2 The Chi-square Test 14.3 A Test of a Hypothesis Concerning Specified Cell Probabilities: A Goodness-of-FitTest 14.4 Contingency Tables 14.5 rx c Tables with Fixed Row or Column Totals 14.6 Other Applications 14.7 Summary Nonparametric Statistics ____ — 573 575 577 582 591 595 597 603 15.1 Introduction 603 15.2 A General Two-Sample Shift Model 604 15.3 The Sign Test for a Paired Experiment 606 15.4 The Wilcoxon Signed-Rank Test fora Paired Experiment 612 15.5 The Use of Ranks for Comparing Two Population Distributions: Independent Random Samples 618 15.6 The Mann-Whitney UTest: Independent Random Samples 621 15.7 The Kruskal-Wallls H Test for the Completely Randomized Design 629 15.8 The Friedman Test for Randomized Block Designs 635 15.9 The Runs Test: A Test for Randomness 641 15.10 Rank Correlation Coefficient 648 15.11 Some General Comments on Nonparametric Statistical Tests 655 Appendix I Matrices - - - - - - ------------- ? ------ 663 A1.1 Matrices and Matrix Algebra 663 A1.2 Addition of Matrices 664 A1.3 Multiplication of a Matrix by a Real Number 665 A1.4 Matrix Multiplication 665 A1.5 Identity Elements 668 A1.6 The Inverse of a Matrix 669 A1.7 The Transpose of a Matrix 670 A1.8 A Matrix Expression for a System of Simultaneous Linear Equations 671 A1.9 Inverting a Matrix 673 A1.10 Solving a System of Simultaneous Linear Equations 678
Contents XV Appendix II Appendix III Common Probability Distributions, Means, Variances, and Moment-generating Functions - 681 A2.1 Discrete Distributions 682 A2.2 Continuous Distributions 683 Tflhlpc 685 Table 1 Binomial Probabilities 685 Table 2 Table of e~ x 689 Table 3 Poisson Probabilities 690 Table 4 Normal Curve Areas 696 Table 5 Percentage Points of the t Distributions 697 Table 6 Percentage Points of the Chi-square Distributions 698 Table 7 Percentage Points of the F Distributions 700 Table 8 Distribution Function of U 710 Table 9 Critical Values of T in the Wilcoxon Matched-Pairs, Signed-Ranks Test 716 Table 10 Distribution of the Total Number of Runs R in Samples of Size (n-,, n 2 ) P(R a) 718 Table 11 Critical Values of Spearman’s Rank Correlation Coefficient 720 Table 12 Random Numbers 721 Answers to Exercises 725 Index 741
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| dewey-full | 519.5 |
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| discipline | Mathematik Wirtschaftswissenschaften |
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| spelling | Mendenhall, William 1925- Verfasser (DE-588)132993791 aut Mathematical statistics with applications William Mendenhall ; Richard L. Scheaffer ; Dennis D. Wackerly 3. ed. Boston, Mass. Duxbury Pr. 1986 XV, 750 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistique mathématique Mathematical statistics Statistik (DE-588)4056995-0 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Statistik (DE-588)4056995-0 s DE-604 Scheaffer, Richard L. Verfasser aut Wackerly, Dennis D. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004025798&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Mendenhall, William 1925- Scheaffer, Richard L. Wackerly, Dennis D. Mathematical statistics with applications Statistique mathématique Mathematical statistics Statistik (DE-588)4056995-0 gnd |
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| title | Mathematical statistics with applications |
| title_auth | Mathematical statistics with applications |
| title_exact_search | Mathematical statistics with applications |
| title_full | Mathematical statistics with applications William Mendenhall ; Richard L. Scheaffer ; Dennis D. Wackerly |
| title_fullStr | Mathematical statistics with applications William Mendenhall ; Richard L. Scheaffer ; Dennis D. Wackerly |
| title_full_unstemmed | Mathematical statistics with applications William Mendenhall ; Richard L. Scheaffer ; Dennis D. Wackerly |
| title_short | Mathematical statistics with applications |
| title_sort | mathematical statistics with applications |
| topic | Statistique mathématique Mathematical statistics Statistik (DE-588)4056995-0 gnd |
| topic_facet | Statistique mathématique Mathematical statistics Statistik Einführung |
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