Modern mathematical statistics with applications / Jay L. Devore, Kenneth N. Berk, Matthew A. Carlton.

Author
Devore, Jay L. [Browse]
Format
Book
Language
English
Εdition
Third edition.
Published/​Created
  • Cham, Switzerland : Springer, [2021]
  • ©2021
Description
1 online resource (981 pages)

Details

Subject(s)
Series
Source of description
Description based on print version record.
Contents
  • Intro -- Preface -- Purpose -- Content and Mathematical Level -- Recommended Coverage -- Revisions for This Edition -- Acknowledgements -- A Final Thought -- Contents -- 1 Overview and Descriptive Statistics -- 1.1 The Language of Statistics -- 1.2 Graphical Methods in Descriptive Statistics -- 1.3 Measures of Center -- 1.4 Measures of Variability -- Supplementary Exercises: (73-96) -- 2 Probability -- 2.1 Sample Spaces and Events -- 2.2 Axioms, Interpretations, and Properties of Probability -- 2.3 Counting Methods -- 2.4 Conditional Probability -- 2.5 Independence -- 2.6 Simulation of Random Events -- Supplementary Exercises: (113-140) -- 3 Discrete Random Variables and Probability Distributions -- 3.1 Random Variables -- 3.2 Probability Distributions for Discrete Random Variables -- 3.3 Expected Values of Discrete Random Variables -- 3.4 Moments and Moment Generating Functions -- 3.5 The Binomial Probability Distribution -- 3.6 The Poisson Probability Distribution -- 3.7 Other Discrete Distributions -- 3.8 Simulation of Discrete Random Variables -- Supplementary Exercises: (138-169) -- 4 Continuous Random Variables and Probability Distributions -- 4.1 Probability Density Functions and Cumulative Distribution Functions -- 4.2 Expected Values and Moment Generating Functions -- 4.3 The Normal Distribution -- 4.4 The Gamma Distribution and Its Relatives -- 4.5 Other Continuous Distributions -- 4.6 Probability Plots -- 4.7 Transformations of a Random Variable -- 4.8 Simulation of Continuous Random Variables -- Supplementary Exercises: (131-159) -- 5 Joint Probability Distributions and Their Applications -- 5.2 Expected Values, Covariance, and Correlation -- 5.3 Linear Combinations -- 5.4 Conditional Distributions and Conditional Expectation -- 5.5 The Bivariate Normal Distribution -- 5.6 Transformations of Multiple Random Variables.
  • 5.7 Order Statistics -- Supplementary Exercises: (122-150) -- 6 Statistics and Sampling Distributions -- 6.1 Statistics and Their Distributions -- 6.2 The Distribution of Sample Totals, Means, and Proportions -- 6.3 The χ2, t, and F Distributions -- 6.4 Distributions Based on Normal Random Samples -- Supplementary Exercises: (59-68) -- Appendix: Proof of the Central Limit Theorem -- 7 Point Estimation -- 7.1 Concepts and Criteria for Point Estimation -- 7.2 The Methods of Moments and Maximum Likelihood -- 7.3 Sufficiency -- 7.4 Information and Efficiency -- Supplementary Exercises: (61-78) -- 8 Statistical Intervals Based on a Single Sample -- 8.1 Basic Properties of Confidence Intervals -- 8.2 The One-Sample t Interval and Its Relatives -- 8.3 Intervals for a Population Proportion -- 8.4 Confidence Intervals for the Population Variance and Standard Deviation -- 8.5 Bootstrap Confidence Intervals -- Supplementary Exercises (71-92) -- 9 Tests of Hypotheses Based on a Single Sample -- 9.1 Hypotheses and Test Procedures -- 9.2 Tests About a Population Mean -- 9.3 Tests About a Population Proportion -- 9.4 P-Values -- 9.5 The Neyman-Pearson Lemma and Likelihood Ratio Tests -- 9.6 Further Aspects of Hypothesis Testing -- Supplementary Exercises: (83-102) -- 10 Inferences Based on Two Samples -- 10.1 The Two-Sample z Confidence Interval and Test -- 10.2 The Two-Sample t Confidence Interval and Test -- 10.3 Analysis of Paired Data -- 10.4 Inferences About Two Population Proportions -- 10.5 Inferences About Two Population Variances -- 10.6 Inferences Using the Bootstrap and Permutation Methods -- Supplementary Exercises: (95-124) -- 11 The Analysis of Variance -- 11.1 Single-Factor ANOVA -- 11.2 Multiple Comparisons in ANOVA -- 11.3 More on Single-Factor ANOVA -- 11.4 Two-Factor ANOVA without Replication -- 11.5 Two-Factor ANOVA with Replication.
  • Supplementary Exercises: (74-84) -- 12 Regression and Correlation -- 12.1 The Simple Linear Regression Model -- 12.2 Estimating Model Parameters -- 12.3 Inferences About the Regression Coefficient β1 -- 12.4 Inferences for the (Mean) Response -- 12.5 Correlation -- 12.6 Investigating Model Adequacy: Residual Analysis -- 12.7 Multiple Regression Analysis -- 12.8 Quadratic, Interaction, and Indicator Terms -- 12.9 Regression with Matrices -- 12.10 Logistic Regression -- Supplementary Exercises: (121-138) -- 13 Chi-Squared Tests -- 13.1 Goodness-of-Fit Tests -- 13.2 Two-Way Contingency Tables -- Supplementary Exercises: (32-43) -- 14 Nonparametric Methods -- 14.1 Exact Inference for Population Quantiles -- 14.2 One-Sample Rank-Based Inference -- 14.3 Two-Sample Rank-Based Inference -- 14.4 Nonparametric ANOVA -- Supplementary Exercises: (49-58) -- 15 Introduction to Bayesian Estimation -- 15.1 Prior and Posterior Distributions -- 15.2 Bayesian Point and Interval Estimation -- Appendix_1 -- Appendix_2 -- Bib1 -- Bib1 -- Index.
ISBN
3-030-55156-3
OCLC
1249072193
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