Holdings: Mathematical statistics

Mathematical statistics:

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Bibliographic Details
Main Authors:	Freund, John E. 1921-2004 (Author), Walpole, Ronald E. (Author)
Format:	Book
Language:	English
Published:	London [u.a.] Prentice-Hall 1980
Edition:	3. ed.
Series:	Prentice-Hall international editions
Subjects:	Mathematical statistics Wahrscheinlichkeitstheorie Statistik Einführung Lehrbuch
Online Access:	Inhaltsverzeichnis
Physical Description:	548 S.
ISBN:	0135620821

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MARC


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adam_text	PREFACE INTRODUCTION /1.1 Historical Background 1 1.2 Mathematical Preliminary: Combinatorial Methods 2 1.3 Mathematical Preliminary: Binomial Coefficients 13 PROBABILITY ^ ^ 2.1 Introduction 24 ^^^ 2.2 Sample Spaces 25 ^•^ 2.3 Events 28 2.4 The Probability of an Event 35 2.5 Some Rules of Probability 39 2.6 Conditional Probability 49 2.7 Independent Events 55 2.8 Bayes Theorem 59 vi Contents PROBABILITY DISTRIBUTIONS f^ 3.1 Random Variables 70 _ ^ 3.2 Discrete Probability Distributions 73 ^ ^ 3.3 Continuous Random Variables 84 3.4 Probability Density Functions 85 3.5 Multivariate Distributions 98 3.6 Marginal Distributions 112 3.7 Conditional Distributions 116 MATHEMATICAL EXPECTATION ^ 4.1 Introduction 127 /¦ 4.2 The Expected Value of a Random Variable 128 jR 4.3 Moments 137 4.4 Chebyshev s Theorem 141 4.5 Moment Generating Functions 144 4.6 Product Moments 151 4.7 Moments of Linear Combinations of Random Variables 156 4.8 Conditional Expectations 159 SPECIAL PROBABILITY DISTRIBUTIONS 5 5.1 Introduction 164 5.2 777e Discrete Uniform Distribution 164 5.3 The Bernoulli Distribution 165 5.4 777e Binomial Distribution 166 5.5 The Negative Binomial and Geometric Distributions 175 5.6 The Hypergeometric Distribution 178 5.7 The Poisson Distribution 181 5.8 77?e Multinomial Distribution 189 5.9 The Multivariate Hypergeometric Distribution 191 SPECIAL PROBABILITY DENSITIES «6.1 Introduction 194 6.2 The Uniform Density 194 6.3 777e Gamma, Exponential, and Chi square Distributions 195 6.4 77?e Beta Distribution 200 6.5 7?7e Normal Distribution 206 Contents vli 6.6 The Normal Approximation to the Binomial Distribution 212 6.7 The Bivariate Normal Distribution 216 FUNCTIONS OF RANDOM VARIABLES pBH 7.1 Introduction 225 ^f 7.2 Distribution Function Technique 226 w 7.3 Transformation of Variable Technique 230 7.4 Moment Generating Function Technique 248 SAMPLING DISTRIBUTIONS »8.1 Introduction 253 8.2 The Distribution of the Mean 255 8.3 777e Distribution of the Mean: Finite Populations 260 8.4 77?e Chi square Distribution 266 8.5 777e t Distribution 270 8.6 77je F Distribution 273 8.7 Crater Statistics 279 DECISION THEORY 9 9.1 Introduction 286 9.2 7/je Theory of Games 288 9.3 Statistical Games 299 9.4 Decision Criteria 303 9.5 777e Minimax Criterion 303 9.6 77?e fiayes Criterion 305 POINT ESTIMATION Tf^± 10 1 Introduction 310 Mmm 10 2 Point Estimation 310 MLW W 10.3 Unbiased Estimators 311 10.4 Consistent Estimators 316 10.5 Sufficient Estimators 318 10.6 The Method of Moments 325 10.7 The Method of Maximum Likelihood 327 10.8 Bayesian Estimators 333 viii Contents INTERVAL ESTIMATION «11.1 Introduction 341 11.2 Confidence Intervals for Means 342 11.3 Confidence Intervals for Differences Between Means 346 11.4 Confidence Intervals for Proportions 352 11.5 Confidence Intervals for Differences Between Proportions 354 11.6 Confidence Intervals for Variances 356 11.7 Confidence Intervals for Ratios of Two Variances 357 HYPOTHESIS TESTING: THEORY W f~M 12.1 Statistical Hypotheses 361 M ^^£ 12 2 Testing a Statistical Hypothesis 363 B.^^ 12.3 Losses and Risks 366 12.4 The Neyman Pearson Lemma 367 12.5 The Power Function of a Test 373 12.6 Likelihood Ratio Tests 377 HYPOTHESIS TESTING: APPLICATIONS WfM 13.1 Introduction 387 Mm~m 13.2 Tests Concerning Means 390 RM_W 13.3 Tests Concerning Differences Between Means 393 13.4 Tests Concerning Variances 399 13.5 Tests Concerning Proportions 403 13.6 Tests Concerning Differences Among k Proportions 406 13.7 Contingency Tables 411 13.8 Goodness of Fit 413 REGRESSION AND CORRELATION M14.1 Regression 419 14.2 Linear Regression 423 14.3 The Method of Least Squares 425 14.4 Normal Regression Analysis 436 14.5 Normal Correlation Analysis 440 Contents ix ANALYSIS OF VARIANCE ~W IU0 15.1 Introduction 452 M^^k 15.2 One Way Analysis of Variance 452 MM^F 15.3 Experimental Design 461 15.4 Two Way Analysis of Variance 463 15.5 Some Further Considerations 472 NONPARAMETRIC METHODS ~WM~ 16.1 Introduction 474 ffim 16.2 The Sign Test Alb MLW F ^ 16.3 The Signed Rank Test 478 16.4 Rank Sum Tests: The U 7esf 480 16.5 Rank Sum Tests: The H Tesf 484 16.6 Tests Sasetf on fluns 488 16.7 77?e ffan/r Correlation Coefficient 492 APPENDIX: THE ALGEBRA OF EVENTS ^J~ 1.1 Boolean Algebra 500 APPENDIX: SUMS AND PRODUCTS TM~TM~ H 1 Rules for Sums and Products 504 UU 11.2 Special Sums 506 STATISTICAL TABLES 508 ANSWERS TO ODD NUMBERED EXERCISES 528 INDEX 543
adam_txt	PREFACE INTRODUCTION /1.1 Historical Background 1 1.2 Mathematical Preliminary: Combinatorial Methods 2 1.3 Mathematical Preliminary: Binomial Coefficients 13 PROBABILITY ^"^ 2.1 Introduction 24 ^^^ 2.2 Sample Spaces 25 ^•^ 2.3 Events 28 2.4 The Probability of an Event 35 2.5 Some Rules of Probability 39 2.6 Conditional Probability 49 2.7 Independent Events 55 2.8 Bayes' Theorem 59 vi Contents PROBABILITY DISTRIBUTIONS f^ 3.1 Random Variables 70 _"^ 3.2 Discrete Probability Distributions 73 ^ ^ 3.3 Continuous Random Variables 84 3.4 Probability Density Functions 85 3.5 Multivariate Distributions 98 3.6 Marginal Distributions 112 3.7 Conditional Distributions 116 MATHEMATICAL EXPECTATION ^ 4.1 Introduction 127 /¦ 4.2 The Expected Value of a Random Variable 128 jR 4.3 Moments 137 4.4 Chebyshev's Theorem 141 4.5 Moment Generating Functions 144 4.6 Product Moments 151 4.7 Moments of Linear Combinations of Random Variables 156 4.8 Conditional Expectations 159 SPECIAL PROBABILITY DISTRIBUTIONS 5 5.1 Introduction 164 5.2 777e Discrete Uniform Distribution 164 5.3 The Bernoulli Distribution 165 5.4 777e Binomial Distribution 166 5.5 The Negative Binomial and Geometric Distributions 175 5.6 The Hypergeometric Distribution 178 5.7 The Poisson Distribution 181 5.8 77?e Multinomial Distribution 189 5.9 The Multivariate Hypergeometric Distribution 191 SPECIAL PROBABILITY DENSITIES «6.1 Introduction 194 6.2 The Uniform Density 194 6.3 777e Gamma, Exponential, and Chi square Distributions 195 6.4 77?e Beta Distribution 200 6.5 7?7e Normal Distribution 206 Contents vli 6.6 The Normal Approximation to the Binomial Distribution 212 6.7 The Bivariate Normal Distribution 216 FUNCTIONS OF RANDOM VARIABLES pBH 7.1 Introduction 225 ^f 7.2 Distribution Function Technique 226 w 7.3 Transformation of Variable Technique 230 7.4 Moment Generating Function Technique 248 SAMPLING DISTRIBUTIONS »8.1 Introduction 253 8.2 The Distribution of the Mean 255 8.3 777e Distribution of the Mean: Finite Populations 260 8.4 77?e Chi square Distribution 266 8.5 777e t Distribution 270 8.6 77je F Distribution 273 8.7 Crater Statistics 279 DECISION THEORY 9 9.1 Introduction 286 9.2 7/je Theory of Games 288 9.3 Statistical Games 299 9.4 Decision Criteria 303 9.5 777e Minimax Criterion 303 9.6 77?e fiayes Criterion 305 POINT ESTIMATION Tf^± 10 1 Introduction 310 Mmm 10 2 Point Estimation 310 MLW W 10.3 Unbiased Estimators 311 10.4 Consistent Estimators 316 10.5 Sufficient Estimators 318 10.6 The Method of Moments 325 10.7 The Method of Maximum Likelihood 327 10.8 Bayesian Estimators 333 viii Contents INTERVAL ESTIMATION «11.1 Introduction 341 11.2 Confidence Intervals for Means 342 11.3 Confidence Intervals for Differences Between Means 346 11.4 Confidence Intervals for Proportions 352 11.5 Confidence Intervals for Differences Between Proportions 354 11.6 Confidence Intervals for Variances 356 11.7 Confidence Intervals for Ratios of Two Variances 357 HYPOTHESIS TESTING: THEORY W f~M 12.1 Statistical Hypotheses 361 M ^^£ 12 2 Testing a Statistical Hypothesis 363 B.^^' 12.3 Losses and Risks 366 12.4 The Neyman Pearson Lemma 367 12.5 The Power Function of a Test 373 12.6 Likelihood Ratio Tests 377 HYPOTHESIS TESTING: APPLICATIONS WfM 13.1 Introduction 387 Mm~m 13.2 Tests Concerning Means 390 RM_W 13.3 Tests Concerning Differences Between Means 393 13.4 Tests Concerning Variances 399 13.5 Tests Concerning Proportions 403 13.6 Tests Concerning Differences Among k Proportions 406 13.7 Contingency Tables 411 13.8 Goodness of Fit 413 REGRESSION AND CORRELATION M14.1 Regression 419 14.2 Linear Regression 423 14.3 The Method of Least Squares 425 14.4 Normal Regression Analysis 436 14.5 Normal Correlation Analysis 440 Contents ix ANALYSIS OF VARIANCE ~W IU0 15.1 Introduction 452 M^^k 15.2 One Way Analysis of Variance 452 MM^F 15.3 Experimental Design 461 15.4 Two Way Analysis of Variance 463 15.5 Some Further Considerations 472 NONPARAMETRIC METHODS ~WM~ 16.1 Introduction 474 ffim 16.2 The Sign Test Alb MLW F ^ 16.3 The Signed Rank Test 478 16.4 Rank Sum Tests: The U 7esf 480 16.5 Rank Sum Tests: The H Tesf 484 16.6 Tests Sasetf on fluns 488 16.7 77?e ffan/r Correlation Coefficient 492 APPENDIX: THE ALGEBRA OF EVENTS ^J~ 1.1 Boolean Algebra 500 APPENDIX: SUMS AND PRODUCTS TM~TM~ H 1 Rules for Sums and Products 504 UU 11.2 Special Sums 506 STATISTICAL TABLES 508 ANSWERS TO ODD NUMBERED EXERCISES 528 INDEX 543
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spellingShingle	Freund, John E. 1921-2004 Walpole, Ronald E. Mathematical statistics Mathematical statistics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd
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title	Mathematical statistics
title_auth	Mathematical statistics
title_exact_search	Mathematical statistics
title_exact_search_txtP	Mathematical statistics
title_full	Mathematical statistics John E. Freund ; Ronald E. Walpole
title_fullStr	Mathematical statistics John E. Freund ; Ronald E. Walpole
title_full_unstemmed	Mathematical statistics John E. Freund ; Ronald E. Walpole
title_short	Mathematical statistics
title_sort	mathematical statistics
topic	Mathematical statistics Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd Statistik (DE-588)4056995-0 gnd
topic_facet	Mathematical statistics Wahrscheinlichkeitstheorie Statistik Einführung Lehrbuch
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work_keys_str_mv	AT freundjohne mathematicalstatistics AT walpoleronalde mathematicalstatistics

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