Mathematical Statistics with Applications in R
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Mathematical Statistics with Applications in R, Second Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining the discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem solving in a logical manner.
This book provides a step-by-step procedure to solve real problems, making the topic more accessible. It includes goodness of fit methods to identify the probability distribution that characterizes the probabilistic behavior or a given set of data. Exercises as well as practical, real-world chapter projects are included, and each chapter has an optional section on using Minitab, SPSS and SAS commands. The text also boasts a wide array of coverage of ANOVA, nonparametric, MCMC, Bayesian and empirical methods; solutions to selected problems; data sets; and an image bank for students.
Advanced undergraduate and graduate students taking a one or two semester mathematical statistics course will find this book extremely useful in their studies.
- Step-by-step procedure to solve real problems, making the topic more accessible
- Exercises blend theory and modern applications
- Practical, real-world chapter projects
- Provides an optional section in each chapter on using Minitab, SPSS and SAS commands
- Wide array of coverage of ANOVA, Nonparametric, MCMC, Bayesian and empirical methods
CHAPTER 2. Basic Concepts from Probability Theory
CHAPTER 3. Additional Topics in Probability
CHAPTER 4. Sampling Distributions
CHAPTER 5. Statistical Estimation
CHAPTER 6. Hypothesis Testing
CHAPTER 7. Goodness-of-Fit Tests Applications
CHAPTER 8. Linear Regression Models
CHAPTER 9. Design of Experiments
CHAPTER 10. Analysis of Variance
CHAPTER 11. Bayesian Estimation Inference
CHAPTER 12. Nonparametric Tests
CHAPTER 13. Empirical Methods
CHAPTER 14. Some Issues in Statistical Applications: An Overview