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
1. Descriptive Statistics 2. Basic Concepts from Probability Theory 3. Additional Topics in Probability 4. Sampling Distributions 5. Estimation 6. Properties of Point Estimation, Hypothesis Testing 7. Linear Regression Models 8. Design of Experiments 9. Analysis of variance 10. Bayesian Estimation and Inference 11. Nonparametric tests 12. Empirical Methods 13. Time-series Analysis 14. Overview of Statistical Applications 15. Appendices 16. Selected Solutions to Exercises
Kandethody M Ramachandran is a Professor of Mathematics and Statistics at the University of South Florida (USF). His research interests are concentrated in the areas of applied probability and statistics. His research publications span a variety of areas such as control of heavy traffic queues, stochastic delay systems, machine learning methods applied to game theory, finance, cyber security, and other areas, software reliability problems, applications of statistical methods to microarray data analysis, and streaming data analysis. He is also, co-author of three books. He is the founding director of the Interdisciplinary Data Sciences Consortium (IDSC). He is extensively involved in activities to improve statistics and mathematics education. He is a recipient of the Teaching Incentive Program award at the University of South Florida. He is also the PI of 2 million dollar grant from NSF, and a co_PI of 1.4 million grant from HHMI to improve STEM education at USF.
Tsokos, Chris P.
Chris P. Tsokos is Distinguished University Professor of Mathematics and Statistics at the University of South Florida. Dr. Tsokos' research has extended into a variety of areas, including stochastic systems, statistical models, reliability analysis, ecological systems, operations research, time series, Bayesian analysis, and mathematical and statistical modelling of global warming, both parametric and nonparametric survival analysis, among others. He is the author of more than 400 research publications in these areas, including Random Integral Equations with Applications to Life Sciences and Engineering, Probability Distribution: An Introduction to Probability Theory with Applications, Mainstreams of Finite Mathematics with Applications, Probability with the Essential Analysis, Applied Probability Bayesian Statistical Methods with Applications to Reliability, and Mathematical Statistics with Applications, among others.
Dr. Tsokos is the recipient of many distinguished awards and honors, including Fellow of the American Statistical Association, USF Distinguished Scholar Award, Sigma Xi Outstanding Research Award, USF Outstanding Undergraduate Teaching Award, USF Professional Excellence Award, URI Alumni Excellence Award in Science and Technology, Pi Mu Epsilon, election to the International Statistical Institute, Sigma Pi Sigma, USF Teaching Incentive Program, and several humanitarian and philanthropic recognitions and awards. He is also a member of several academic and professional societies, and serves as Honorary Editor, Chief-Editor, Editor or Associate Editor for more than twelve academic research journals. Prof. Tsokos has directed the doctoral research and been the mentor of more than 65 students.