Probability and Statistics with R

✍ Scribed by Arnholt, Alan T.; Militino, Ana F.; Ugarte, Maria Dolores

• Publisher: CRC Press
• Year: 2008
• Tongue: English
• Leaves: 710
• Series: EBL Schweitzer
• Edition: Online-Ausg
• Category: Library

✦ Synopsis

Front cover; Chapter 1: A Brief Introduction to S; The Basics of S; Using S; Data Sets; Data Manipulation; S Structures; Mathematical Operations; Vectors; Sequences; Reading Data; Using scan(); Using read.table(); Using write(); Using dump() and source(); Logical Operators and Missing Values; Matrices; Vector and Matrix Operations; Arrays; Lists; Data Frames; Tables; Functions Operating on Factors and Lists; Probability Functions; Creating Functions; Programming Statements; Graphs; Problems; Chapter 2: Exploring Data; What Is Statistics?; Data; Displaying Qualitative Data; Tables; Barplots.

Dot ChartsPie Charts; Displaying Quantitative Data; Stem-and-Leaf Plots; Strip Charts (R Only); Histograms; Summary Measures of Location; The Mean; The Median; Quantiles; Hinges and Five-Number Summary; Boxplots; Summary Measures of Spread; Range; Interquartile Range; Variance; Bivariate Data; Two-Way Contingency Tables; Graphical Representations of Two-Way Contingency Tables; Comparing Samples; Relationships between Two Numeric Variables; Correlation; Sorting a Data Frame by One or More of Its Columns; Fitting Lines to Bivariate Data; Multivariate Data (Lattice and Trellis Graphs).

Arranging Several Graphs on a Single PagePanel Functions; Problems; Chapter 3: General Probability and Random Variables; Introduction; Counting Rules; Sampling With Replacement; Sampling Without Replacement; Combinations; Probability; Sample Space and Events; Set Theory; Interpreting Probability; Relative Frequency Approach to Probability; Axiomatic Approach to Probability; Conditional Probability; The Law of Total Probability and Bayes' Rule; Independent Events ; Random Variables; Discrete Random Variables; Mode, Median, and Percentiles; Expected Values of Discrete Random Variables; Moments.

VarianceRules of Variance; Continuous Random Variables; Numerical Integration with S; Mode, Median, and Percentiles; Expectation of Continuous Random Variables; Markov's Theorem and Chebyshev's Inequality; Weak Law of Large Numbers; Skewness; Moment Generating Functions; Problems; Chapter 4: Univariate Probability Distributions; Introduction; Discrete Univariate Distributions; Discrete Uniform Distribution; Bernoulli and Binomial Distributions; Poisson Distribution; Geometric Distribution; Negative Binomial Distribution; Hypergeometric Distribution; Continuous Univariate Distributions.

Uniform Distribution (Continuous)Exponential Distribution; Gamma Distribution; Hazard Function, Reliability Function, and Failure Rate; Weibull Distribution; Beta Distribution; Normal (Gaussian) Distribution; Problems; Chapter 5: Multivariate Probability Distributions; Joint Distribution of Two Random Variables; Joint pdf for Two Discrete Random Variables; Joint pdf for Two Continuous Random Variables; Independent Random Variables; Several Random Variables; Conditional Distributions; Expected Values, Covariance, and Correlation; Expected Values; Covariance; Correlation.

-Technometrics, May 2009, Vol. 51, No. 2 The book is comprehensive and well written. The notation is clear and the mathematical derivations behind nontrivial equations and computational implementations are carefully explained. Rather than presenting a collection of R scripts together with a summary of relevant theoretical results, this book offers a well-balanced mix of theory, examples and R code.-Raquel Prado, University of California, Santa Cruz, The American Statistician, February 2009... an impressive book ... Overall, this is a good reference book with comprehensive coverage of the details. Read more...

Abstract: Front cover; Chapter 1: A Brief Introduction to S; The Basics of S; Using S; Data Sets; Data Manipulation; S Structures; Mathematical Operations; Vectors; Sequences; Reading Data; Using scan(); Using read.table(); Using write(); Using dump() and source(); Logical Operators and Missing Values; Matrices; Vector and Matrix Operations; Arrays; Lists; Data Frames; Tables; Functions Operating on Factors and Lists; Probability Functions; Creating Functions; Programming Statements; Graphs; Problems; Chapter 2: Exploring Data; What Is Statistics?; Data; Displaying Qualitative Data; Tables; Barplots.

Dot ChartsPie Charts; Displaying Quantitative Data; Stem-and-Leaf Plots; Strip Charts (R Only); Histograms; Summary Measures of Location; The Mean; The Median; Quantiles; Hinges and Five-Number Summary; Boxplots; Summary Measures of Spread; Range; Interquartile Range; Variance; Bivariate Data; Two-Way Contingency Tables; Graphical Representations of Two-Way Contingency Tables; Comparing Samples; Relationships between Two Numeric Variables; Correlation; Sorting a Data Frame by One or More of Its Columns; Fitting Lines to Bivariate Data; Multivariate Data (Lattice and Trellis Graphs).

Arranging Several Graphs on a Single PagePanel Functions; Problems; Chapter 3: General Probability and Random Variables; Introduction; Counting Rules; Sampling With Replacement; Sampling Without Replacement; Combinations; Probability; Sample Space and Events; Set Theory; Interpreting Probability; Relative Frequency Approach to Probability; Axiomatic Approach to Probability; Conditional Probability; The Law of Total Probability and Bayes' Rule; Independent Events ; Random Variables; Discrete Random Variables; Mode, Median, and Percentiles; Expected Values of Discrete Random Variables; Moments.

VarianceRules of Variance; Continuous Random Variables; Numerical Integration with S; Mode, Median, and Percentiles; Expectation of Continuous Random Variables; Markov's Theorem and Chebyshev's Inequality; Weak Law of Large Numbers; Skewness; Moment Generating Functions; Problems; Chapter 4: Univariate Probability Distributions; Introduction; Discrete Univariate Distributions; Discrete Uniform Distribution; Bernoulli and Binomial Distributions; Poisson Distribution; Geometric Distribution; Negative Binomial Distribution; Hypergeometric Distribution; Continuous Univariate Distributions.

Uniform Distribution (Continuous)Exponential Distribution; Gamma Distribution; Hazard Function, Reliability Function, and Failure Rate; Weibull Distribution; Beta Distribution; Normal (Gaussian) Distribution; Problems; Chapter 5: Multivariate Probability Distributions; Joint Distribution of Two Random Variables; Joint pdf for Two Discrete Random Variables; Joint pdf for Two Continuous Random Variables; Independent Random Variables; Several Random Variables; Conditional Distributions; Expected Values, Covariance, and Correlation; Expected Values; Covariance; Correlation.

-Technometrics, May 2009, Vol. 51, No. 2 The book is comprehensive and well written. The notation is clear and the mathematical derivations behind nontrivial equations and computational implementations are carefully explained. Rather than presenting a collection of R scripts together with a summary of relevant theoretical results, this book offers a well-balanced mix of theory, examples and R code.-Raquel Prado, University of California, Santa Cruz, The American Statistician, February 2009... an impressive book ... Overall, this is a good reference book with comprehensive coverage of the details

✦ Table of Contents

Content: A Brief Introduction to S The Basics of S Using S Data Sets Data Manipulation Probability Functions Creating Functions Programming Statements Graphs Exploring Data What Is Statistics? Data Displaying Qualitative Data Displaying Quantitative Data Summary Measures of Location Summary Measures of Spread Bivariate Data Multivariate Data (Lattice and Trellis Graphs) General Probability and Random Variables Introduction Counting Rules Probability Random Variables Univariate Probability Distributions Introduction Discrete Univariate Distributions Continuous Univariate Distributions Multivariate Probability Distributions Joint Distribution of Two Random Variables Independent Random Variables Several Random Variables Conditional Distributions Expected Values, Covariance, and Correlation Multinomial Distribution Bivariate Normal Distribution Sampling and Sampling Distributions Sampling Parameters Estimators Sampling Distribution of the Sample Mean Sampling Distribution for a Statistic from an Infinite Population Sampling Distributions Associated with the Normal Distribution Point Estimation Introduction Properties of Point Estimators Point Estimation Techniques Confidence Intervals Introduction Confidence Intervals for Population Means Confidence Intervals for Population Variances Confidence Intervals Based on Large Samples Hypothesis Testing Introduction Type I and Type II Errors Power Function Uniformly Most Powerful Test â -Value or Critical Level Tests of Significance Hypothesis Tests for Population Means Hypothesis Tests for Population Variances Hypothesis Tests for Population Proportions Nonparametric Methods Introduction Sign Test Wilcoxon Signed-Rank Test The Wilcoxon Rank-Sum or the Mann-Whitney U-Test The Kruskal-Wallis Test Friedman Test for Randomized Block Designs Goodness-of-Fit Tests Categorical Data Analysis Nonparametric Bootstrapping Permutation Tests Experimental Design Introduction Fixed-Effects Model Analysis of Variance (ANOVA) for the One-Way Fixed-Effects Model Power and the Noncentral F Distribution Checking Assumptions Fixing Problems Multiple Comparisons of Means Other Comparisons among the Means Summary of Comparisons of Means Random-Effects Model (Variance Components Model) Randomized Complete Block Design Two-Factor Factorial Design Regression Introduction Simple Linear Regression Multiple Linear Regression Ordinary Least Squares Properties of the Fitted Regression Line Using Matrix Notation with Ordinary Least Squares The Method of Maximum Likelihood The Sampling Distribution of ss ANOVA Approach to Regression General Linear Hypothesis Model Selection and Validation Interpreting a Logarithmically Transformed Model Qualitative Predictors Estimation of the Mean Response for New Values Xh Prediction and Sampling Distribution of New Observations Yh(new) Simultaneous Confidence Intervals Appendix A: S Commands Appendix B: Quadratic Forms and Random Vectors and Matrices Quadratic Forms Random Vectors and Matrices Variance of Random Vectors References Index Problems appear at the end of each chapter.