# Probability and Statistics with R

## Second Edition

María Dolores Ugarte, Ana F. Militino, and Alan T. Arnholt

Practical and Visually Appealing with Clear Examples and Fully Detailed Proofs

Probability and Statistics with R, Second Edition shows how to solve various statistical problems using both parametric and nonparametric techniques via the open source software R. It provides numerous real-world examples, carefully explained proofs, end-of-chapter problems, and illuminating graphs to facilitate the hands-on comprehension.

Delves into Many Probability and Statistical Topics

Integrating theory with practice, the text briefly introduces the syntax, structures, and functions of the R language, before covering important graphical and numerical methods of exploring data. The package ggplot2 is used throughout the book to create graphs. The next several chapters elucidate probability and random variables topics, including univariate and multivariate distributions. After exploring sampling distributions, the authors discuss point estimation, confidence intervals, hypothesis testing, and a wide range of nonparametric methods, spotlighting the bootstrap and permutation tests. The book also presents fixed- and random-effects models as well as randomized block and two-factor factorial designs in a chapter on experimental design. The final chapter describes simple and multiple regression analyses with an emphasis on model validation.

Cohesively Incorporates Statistical Theory with R Implementation

This comprehensive book presents extensive treatments of data analysis using parametric and nonparametric techniques. It effectively links statistical concepts with R procedures, empowering the reader to solve a vast array of statistical problems with R.

Features

Provides real-world examples of how R can be used to solve problems in probability and statistics, along with an overview on how to use R.

Explains the mathematics behind computational implementations.

Covers both traditional methods and nonparametric techniques, including goodness-of-fit tests, categorical data analysis, nonparametric bootstrapping, and permutation tests.

Uses regression analysis procedures to solve three interesting case studies based on real data.

Presents thoroughly worked-out derivations, detailed graphs, and abundant problems.

Provides the PASWR2 package, which contains data sets and functions from the text.

• 1.   What is R?
• 2.   Exploring Data
• 3.   General Probability and Random Variables
• 4.   Univariate Probability Distributions
• 5.   Multivariate Probability Distributions
• 6.   Sampling and Sampling Distributions
• 7.   Point Estimation
• 8.   Confidence Intervals
• 9.   Hypothesis Testing
• 10.   Nonparametric Methods
• 11.   Experimental Design
• 12.   Regression

The book was published July 22, 2015.

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María Dolores Ugarte has a degree in Mathematics from the University of Zaragoza, Spain, and a Ph.D. in Statistics from the Public University of Navarre (UPNA), Spain. She completed her postdoctoral training in the Department of Mathematics and Statistics at Simon Fraser University, Canada. She is a full professor in the Department of Statistics and Operations Research at the Public University of Navarre and has taught numerous statistics courses at the undergraduate, masters, and doctoral level. In 2007, she received the INNOLEC Lectureship Award granted by the Faculty of Science, Masaryk University (Czech Republic), and in 2008 received a rating of "Excellent Teacher" from UPNA. She has worked as an associate editor or member of the editorial board with Journal of the Royal Statistical Society Series A, Statistical Modelling, Test, Computational Statistics and Data Analysis, and Spatial and Spatio-temporal Epidemiology.

Ana F. Militino has a degree in Mathematics from the University of Zaragoza, Spain, and a Ph.D. in Statistics from the University of Extremadura, Spain. She has been a visiting professor at Oxford University (1994) and at Simon Fraser University, Canada (1997 and 1998). She is a full professor of Statistics at the Public University of Navarre, Spain. She teaches statistics in undergraduate and graduate programs. In 2010, she received the John Griffiths teaching award from the International Association of Mathematical Geology. Ana is co-editor in chief of TEST, the journal of the Spanish Statistical Society.

Alan T. Arnholt received a B.S. in the Mathematics of Operations Research from the United States Military Academy, West Point, New York, an M.S. in Applied Statistics from the University of Northern Colorado, USA, and a Ph.D. in Applied Statistics from the University of Northern Colorado, USA. He is a full professor in the Department of Mathematical Sciences at Appalachian State University, where he has taught undergraduate and graduate statistics since 1993. Alan enjoys spending time with his wife and two daughters.