For courses in Mathematical Statistics.
Renowned for its high-quality, real-world case studies and examples, this highly structured text is designed to allow students with an established mathematics background to pursue a more rigorous, advanced treatment of probability and statistics. It shows HOW to use statistical methods, WHEN to use them, and reinforces the calculus that students have covered in previous courses.
- NEW - A chapter on experimental design (Ch. 8)—Placed between coverage of the Normal Distribution and Two-Sample Problems. Delineates how one experimental design differs from another and the statistical consequences of those differences.
- NEW - Minitab sections—At the end of chapters.
- NEW - Case studies and examples have been updated and revised.
- NEW - Exercise sets considerably expanded—Nearly 50% more in some chapters.
- NEW - Cover pages include a chart of densities, moments, and moment generating functions.
- NEW - Additional simulations and Monte Carlo studies.
- NEW - Rearrangement of the material on special distributions, estimation, and hypothesis testing (Chs. 4, 5, and 6)—Ch. 4 now addresses more fully why certain measurements are described by particular density functions, gives more attention to relationships between pdfs (e.g., the Poisson and the exponential), and better separates discrete and continuous variables. Defines the exponential density explicitly (and standardizes its form throughout the text). Section 5.8 on methods of estimating parameters has been moved to the beginning of the chapter to help users who do not intend to do much with the theory of point estimation. Simulations help to motivate the mathematical principles of estimation. Ch. 6 has been completely redone with hypothesis testing introduced in the context of the normal H0: …m = …m rather than H0: p = p0. The discreteness of the binomial interferes with the students' ability to understand the decision making process.
- NEW - A complete Solutions Manual in response to user demand.
- Superior treatment of real-world data—Uses case studies and practical worked-out examples to motivate statistical reasoning and demonstrate the application of statistical methods to a wide variety of real-world situations.
- Sound, systematic coverage of the theoretical aspects of mathematical statistics—Introduces critically important concepts at different “levels” throughout the text—beginning with an informal introduction and progressing to more detailed discussions as the concept arises in later chapters.
- Provides prerequisite mathematical material in an accessible way—Reviews calculus as necessary throughout the presentation.
- A chapter on experimental design (Ch. 8)—Placed between coverage of the Normal Distribution and Two-Sample Problems. Delineates how one experimental design differs from another and the statistical consequences of those differences.
- Minitab sections—At the end of chapters.
- Case studies and examples have been updated and revised.
- Exercise sets considerably expanded—Nearly 50% more in some chapters.
- Cover pages include a chart of densities, moments, and moment generating functions.
- Additional simulations and Monte Carlo studies.
- Rearrangement of the material on special distributions, estimation, and hypothesis testing (Chs. 4, 5, and 6)—Ch. 4 now addresses more fully why certain measurements are described by particular density functions, gives more attention to relationships between pdfs (e.g., the Poisson and the exponential), and better separates discrete and continuous variables. Defines the exponential density explicitly (and standardizes its form throughout the text). Section 5.8 on methods of estimating parameters has been moved to the beginning of the chapter to help users who do not intend to do much with the theory of point estimation. Simulations help to motivate the mathematical principles of estimation. Ch. 6 has been completely redone with hypothesis testing introduced in the context of the normal H0: …m = …m rather than H0: p = p0. The discreteness of the binomial interferes with the students' ability to understand the decision making process.
- A complete Solutions Manual in response to user demand.
(NOTE: Each chapter except Ch. 1 begins with an Introduction.)
1. Introduction.
A Brief History. Some Examples. A Chapter Summary.
2. Probability.
Sample Spaces and the Algebra of Sets. The Probability Function. Discrete Probability Functions. Continuous Probability Functions. Conditional Probability. Independence. Repeated Independent Trials. Combinatorics. Combinatorial Probability.
3. Random Variables.
The Probability Density Function. The Hypergeometric and Binomial Distributions. The Cumulative Distribution Function. Joint Densities. Independent Random Variables. Combining and Transforming Random Variables. Order Statistics. Conditional Densities. Expected Values. Properties of Expected Values. The Variance. Properties of Variances. Chebyshev's Inequality. Higher Moments. Moment-Generating Functions. Appendix 3.A.1: MINITAB Applications.
4. Special Distributions.
The Poisson Distribution. The Normal Distribution. The Geometric Distribution. The Negative Binomial Distribution. The Gamma Distribution. Appendix 4.A.1: MINITAB Applications. Appendix 4.A.2: A Proof of the Central Limit Theorem.
5. Estimation.
Estimating Parameters: The Method of Maximum Likelihood and the Method of Moments. Interval Estimation. Properties of Estimators. Minimum-Variance Estimators: The Cramer-Rao Lower Bound. Sufficiency. Consistency. Appendix 5.A.1: MINITAB Applications.
6. Hypothesis Testing.
The Decision Rule. Testing Binomial Data—H0: p = p 0. Type I and Type II Errors. A Notion of Optimality: The Generalized Likelihood Ratio.
7. The Normal Distribution.
Point Estimates for …m and …s2. The …c2 Distribution; Inferences about …s2. The F and t Distributions. Drawing Inferences about …m. Appendix 7.A.1: MINITAB Applications. Appendix 7.A.2: Some Distribution Results for Y and S 2. Appendix 7.A.3: A Proof of Theorem 7.3.5. A Proof That the One-Sample t Test Is a GLRT.
8. Types of Data: A Brief Overview.
Classifying Data.
9. Two-Sample Problems.
Testing H 0: …mx = …mY—The Two-Sample t Test. Testing H0: …s2x = …s2Y—The F Test. Binomial Data: Testing H 0: px = py. Confidence Intervals for the Two-Sample Problem. Appendix 9.A.1: A Derivation of the Two-Sample t Test (A Proof of Theorem 9.2.2.). Appendix 9.A.2: Power Calculations for a Two-Sample t Test. Appendix 9.A.3: MINITAB Applications.
10. Goodness-of-Fit Tests.
The Multinomial Distribution. Goodness-of-Fit Tests: All Parameters Known. Goodness-of-Fit Tests: Parameters Unknown. Contingency Tables. Appendix 10.A.1: MINITAB Applications.
11. Regression.
The Method of Least Squares. The Linear Model. Covariance and Correlation. The Bivariate Normal Distribution. Appendix 11.A.1: MINITAB Applications. Appendix 11.A.2: A Proof of Theorem 11.3.3.
12. The Analysis of Variance.
The F Test. Multiple Comparisons: Tukey's Method. Testing Subhypotheses with Orthogonal Contrasts. Data Transformations. Appendix 12.A.1: MINITAB Applications. Appendix 12.A.2: A Proof of Theorem 12.2.2. Appendix 12.A.3: The Distribution of <$E{ down 12 SSTR/ up 12 (k-1)} over { down 12 SSE/ up 12 (n-k)}> When H1 Is True.
13. Randomized Block Designs.
The F Test for a Randomized Block Design. The Paired t Test. Appendix 13.A.1: MINITAB Applications.
14. Nonparametric Statistics.
The Sign Test. The Wilcoxon Signed Rank Test. The Kruskal-Wallis Test. The Friedman Test. Appendix 14.A.1: MINITAB Applications.
Appendix: Statistical Tables. Answers to Selected Odd-Numbered Questions. Bibliography. Index.