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Statistics: probability, inference, and decision

Author: Winkler, Robert L. ; Hays, William Lee Series: Series in quantitative methods for decision making Publisher: Holt, Rinehart and Winston, 1975.Edition: 2nd ed.Language: EnglishDescription: 889 p. : Graphs/Ill. ; 24 cm.ISBN: 0030140110Type of document: BookNote: Doriot: for 2016-2017 coursesBibliography/Index: Includes bibliographical references and index List(s) this item appears in: Textbooks for Probability and Statistics A / Spyros Zoumpoulis / PhD 2016-2017
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Item type Current location Collection Call number Status Date due
Book Doriot Library
Main Collection
Print QA276 .W55 1975
(Browse shelf)
001365749
Available
Book Doriot Library
Main Collection
Print QA276 .W55 1975
(Browse shelf)
001352671
Available
Book Doriot Library
Main Collection
Print QA276 .W55 1975
(Browse shelf)
000199822
Available
Book Tanoto Library
Textbook Collection (PhD)
Print QA276 .W55 1975
(Browse shelf)
900232562
Consultation only
Book Tanoto Library
Textbook Collection (PhD)
Print QA276 .W55 1975
(Browse shelf)
900203523
Available

Doriot: for 2016-2017 courses

Includes bibliographical references and index

Digitized

CONTENTS Statistics: Probability, Inference, and Decision Statistics: Probability, Inference, and Decision Preface Introduction 1 vii 1 4 Sets and Functions Sets 4 Finite and Infinite Sets 6 Universal Sets and the Empty Set 7 Subsets 8 The Union of Sets 10 The Intersection of Sets 12 The Complement of a Set 15 The Difference Between Two Sets 16 The Algebra of Sets 17 Set Products and Relations 20 The Domain and Range of a Relation 24 Functional Relations 25 Variables and Functional Notation 28 Continuous Variables and Functions 31 Functions and Precise Prediction 32 Exercises 33 2 Elementary Probability Theory 2.1 2.2 2.3 Simple Experiments 42 Events 43 Events as Sets 44 Probability Functions 46 A Special Case: Equally Probable Elementary Events 52 Computing Probabilities 54 Sequences of Events 55 Sequences: Counting Rules 1 and 2 56 Permutations: Counting Rules 3 and' 4 57 Combinations: Counting Rules 5 and 6 59 Some Examples: Poker Hands 61 The Relative Frequency Interpretation of Probability 64 The Law of Large Numbers 65 An Example of Simple Statistical Inference 69 The Subjective Interpretation of Probability 71 Probabilities, Lotteries, and Betting Odds 74 Probability and Decision Making 80 Conditional Probability 83 Relationships Among Conditional, Joint, and Marginal Probabilities 88 Bayed Theorem 93 Independence 98 Exercises 1Q2 , Probability Distributions Random Variables 116 Probability Distributions 118 Discrete Random Variables 121 Probability Distributions of Discrete Random Variables 125 Continuous Random Variables 127 Probability Distributions of Continuous Random Variables 128 Cumulative Distribution Functions 135 Summary Measures of Probability Distributions 140 The Expectation of a Random Variable 141 The Algebra of Expectations 144 Measures of Central Tendency: The Mean 147 The Median 150 The Mode 153 Relations Between Central Tendency Measures and the "Shapes" of Distributions 154 Measures of Dispersion : The Variance 159 The Standard Deviation 164 The Mean as the "Origin" for the Variance 166 The Relative Location of a Value in a Probability Distribution: Standardized Random Variables 167 Chebyshev's Inequality 169 Moments of a Distribution 172 Joint Probability Distributions 173 3.22 3.23 Independence of Random Variables 181 Moments of Conditional and Joint Distributions Exercises 189 184 4 Special Probability Distributions The Bernoullj Process 203 Number of Successes as a Random Variable: The Binomial Distribution 206 The Mean and Variance of the Binomial Distribution 212 The Form of a Binomial Distribution 215 The Binomial as a Sampling Distribution 216 A Preview of a Use of the Binomial Distribution 218 Number of Trials as a Random Variable: The Pascal and Geometric Distributions 220 The Multinomial Distribution 223 The Hypergeometric Distribution 224 The Poisson Process and Distribution 227 The Poisson Approximation to the Binomial 232 Summary of.Special Discrete Distributions 233 The Normal Distribution 236 Computing Probabilities for the Normal Distribution 239 The Importance of the Normal Distribution 244 The Normal Approximation to the Binomial 246 The Theory of the Normal Distribution of Error 251 The Exponential Distribution 252 The Uniform Distribution 255 Summary of Special Continuous Distributions 258 Exercises 259 5 Frequency and Sampling Distributions Random Sampling 273 Random Number Tables 274 Measurement Scales 277 Frequency Distributions 282 Grouped Distributions 285 Class Interval Size, Class Limits, and Midpoints of Class Intervals 287 Graphs of Distributions: Histograms 290 Frequency Pokgons 293 Cumulative Frequency Distributions 294 Measures of Central Tendency for Frequency Distributions 296 Measures of Dispersion for Frequency Distributions 299 Populations, Parameters, and Statistics 302 Sampling Distributions 303 5.14 5.15 5.16 5.17 5.18 5.19 The Mean and Variance of a Sampling Distribution 306 Statistical Properties of Normal Population Distributions: Independence of Sample Mean and Variance 309 Distributions of Linear Combinations of Variables 310 The Central Limit Theorem 314 The Uses of Frequency and Sampling Distributions 319 To What Populations Do Our Inferences Refer? 320 Exercises 321 6 Estimation Sample Statistics as Estimators 334 Unbiasedness 335 Consistency 338 Relative Efficiency 340 Sufficiency 342 Methods for Determining Good Estimators 343 The Principle of Maximum Likelihood 345 The Method of Moments 350 Parameter Estimates Based on Pooled Samples 352 Sampling from Finite Populptions 353 Interval Estimation: Confidence Intervals 354 Confidence Intervals for the Mean when aZ is Known 358 The Problem of Unknown ug:The T Distribution 362 The Concept of Degrees of Freedom 367 Confidence Intervals for the Mean when u2is Unknown 368 Confidence Intervals for Differences Between Means 369 Approximate Confidence Intervals for Proportions 374 The Chi-square Distribution 375 The Distribution of the Sample Variance from a Normal Population 381 Confidence Intervals for the Variance and Standard Deviation 383 The F Distribution 385 Confidence Intervals for Ratios of Variances 388 Relationships Among the Theoretical Sampling Distributions 389 Exercises 391 7 Hypothesis Testing 7.1 7.2 7.3 7.4 7.5 7.6 7.7 Statistical Hypotheses 402 Choosing a Way to Decide Between Two Exact Hypotheses 403 Type I and Type I1 Errors 410 Conventional Decision Rules 413 Deciding Between Two Hypotheses About a Mean 415 Likelihood Ratios and Hypothesis Testing 420 The Power of a Statistical Test 426 The Effect of a! and Sample Size on Power 429 Testing Inexact Hypotheses 431 One-Tailed Rejection Regions 435 Two-Tailed Tests of Hypotheses 436 One- and Two-Tailed Tests: Power, Operating Characteristic, and Error Curves 439 Reporting the Results of Tests 441 Sample Size and p-Values 444 Tests Concerning Means 447 Tests Concerning Differences Between Means 448 Paired Observations 450 The Power of T Tests 452 Testing Hypotheses About a Single Variance 453 Testing Hypotheses About Two Variances 455 Exercises 456 8 Bayesian Inference Rayes' Theorem for Discrete Random Variables 472 An Example af Bayesian Inference and Decision 475 The Assessment of Prior Probabilities 482 The Assessment of Likelihoods 485 Bayes' Theorem for Continuous Random Variables 493 Conjugate Prior Distributions for the Bernoulli Process 498 The Use of Beta Prior Distributions: An Example 503 Conjugate Prior Distributions for the Normal Process 507 The Use of Normal Prior Distributions: An Example 509 Conjugate Prior Distributions for Other Processes 512 The Assessment of Prior Distributions 513 Discrete Approximations of Continuous Probability Models 518 Representing a Diffuse Prior State 521 Diffuse Prior Distributions and Scientific Reporting 523 The Posterior Distribution and Estimation 525 Prior and Posterior Odds Ratios 527 The Posterior Distribution and Hypothesis Testing 532 The Posterior Distribution and Two-Tailed Tests 534 Exercises 536 9 Decision Theory 9.1 9.2 9.3 9.4 9.5 Certainty Versus Uncertainty 551 Payoffs and Losses 553 Nonprobabilistic Criteria for Decision Making Under Uncertainty 558 Probabilistic Criteria for Decision Making Under Uncertainty 562 Utility 566 The Assessment of Utility Functions 569 Shapes of Utility Functions 573 A Formal Statement of the Decision Problem 577 Decision Making Under Uncertainty: An Example 579 Terminal Decisions and Preposterior Decisions 586 The Expected Value of Perfect Information 588 The Expected Value of Sample Information 591 Sample Size and ENGS 598 Preposterior Analysis: An Example 600 Linear Payoff Functions: The Two-Action Problem 606 Decision Theory and Point Estimation 613 Point Estimation: Linear and Quadratic Loss Functions 616 Decision Theory and Hypothesis Testing 621 The Different Approaches to Statistical Problems 625 Exercises 627 10 Regression and Correlation Correlation 644 The Bivariate Normal Distribution 650 Inferences in Correldion Problems 652 An Example of a Correlation Problem 655 The Regression Curve 658 Linear Regression 661 Estimating the Regression Line 664 The Idea of Regression Toward the Mean 670 Inferences in Regression Problems 672 An Example of a Regression Problem 678 Multiple Regression 683 Multiple and Partial Correlation 685 Multiple Regression in Matrix Form 690 An Example of a Multiple Regression Problem 695 Computers and Multiple Regression 700 Nonlinear Regression 701 Applying Least Squares in Nonlinear Regression 706 Transformation of Variables in Nonlinear Regression 708 Time Series and Regression Analpis 713 A Brief Look a t Econometrics: Other Problems in Regression 715 Exercises 717 11 Sampling Theory, Experimental Design, and Analysis of Variance 11.1 11.2 11.3 Sampling from Finite Populations 730 Stratified Sampling 735 Cluster Sampling 739 Other Topics in Sampling Theory 741 Sample Design and Experimental Design 744 Analysis of Variance: The One-Factor Model 747 Partitioning the Variation in an Experiment 751 The F Test in the One-Factor Model 755 An Example of a One-Factor Analysis of Variance 758 Estimating the Strength of a Statistical Relation in the One-Factor Model 764 Analysis of Variance: The Two-Factor Model 767 Partitioning the Variation in the Two-Factor Model 772 F Tests in the Two-Factor Model 775 Computing Forms for the Two-Factor Model 779 An Example of a Two-Factor Analysis of Variance 783 Estimating Strength of Association in the Two-Factor Model 786 The Fixed-Effects Model and the Random-Effects Model 789 Regression and Analysis of Variance: The General Linear Model 792 Testing for Linear and Nonljnear Regression 794 The Analysis of Variance and the General Problem of Experimental Design 800 Exercise% 804. 12 Nonparametric Methods Methods Involving Categorical Data 816 Comparing Sample and Population Distributions: Goodness of Fit 817 A Special Problem: A Goodness-of-Fit Test for a Normal Distribution 822 Pearson x2 Tests of Association 825 Measures of Association in Contingency Tables 831 The Phi Coefficient and Indices of Contingency 833 A Measure of Predictive Association for Categorical Data 835 Information Theory and the Analysis of Contingency Tables 840 Order Statistics 842 The Komogorov-Smirnov Test for Goodness of Fit 845 The Wald-Wolfowitz "Runs" Test for Two Samples 848 The Mann-Whitney Test for Two Independent Samples 852 The Sign Test for Matched Pairs 855 The Wilcoxon Test for Two Matched Samples 856Comparing J Independent Groups: The Median Test 859 The Kruskal-Wallis "Analysis of Variance" by Ranks 862 The Friedman Test for J Matched Groups 864 Rank-Order Correlation Methods 866 The Spearman Rank Correlation Coefficient 867 The Kendall Tau Coefficient 871 Kendall's Coefficient of Concordance 874 Exercises 876 Appendix A Some Common Differentiation and Integration Formulas i Appendix B Matrix Algebra iv Tables Table Table Table Table Table Table Table Table Table Table Table Table Table Table I. 11. 111. IV. V. VI. VII. VIII. IX. X. XI. XII. XIII. XIV. xiii Cumulative Standard Normal Probabilities xiii Fractiles of the T Distribution xv Fractiles of the X2 Distribution xvi Fractiles of the F Distribution xviii Binomial Probabilities xxi Poisson Probabilities xxvi Standard Normal Density Function xxxi Random Digits xxxiii The Transformatioq of r t o w xxxiv Unit Normal Linear Loss Integral x m i Fractiles of D in the Kolmogorov-Smirnov One-Sample Test xxxviii Binomial Coefficients xxxix Factorials of Integers xl Powers and Roots xli References and Suggestions for Further Reading Answers to Selected Exercises Index li Iv lxvi

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