A course in statistics with R. (2016)

• Record Type: Book
• Further Information: Note: Prabhanjan Tattar, Suresh Ramaiah, B.G. Manjunath.
• Authors: Tattar, Prabhanjan, 1979-; Ramaiah, Suresh, 1979-; Manjunath, B. G, 1981-
• Contents: I The Preliminaries 1 1 Why R? 2 1.1 Why R? 2 1.2 R Installation 4 1.3 There is Nothing Such as PRACTICALS 5 1.4 Data Sets in R and Internet 6 1.4.1 List of Web-sites Containing DATA SETS 7 1.4.2 Antique Datasets 8 1.5 http://cran.r-project.org 10 1.5.1 http://r-project.org 11 1.5.2 http://www.cran.r-project.org/web/views/ 11 1.5.3 Is subscribing to R-Mailing List useful? 12 1.6 R and Its Interface with Other Software 12 1.7 help and/or ? 13 1.8 R Books 14 1.9 A Road Map 15 2 The R Basics 18 2.1 Introduction 18 2.2 Simple Arithmetics and a Little Beyond 19 2.2.1 Absolute Values, Remainders, etc 20 2.2.2 round, floor, etc 21 2.2.3 Summary Functions 21 2.2.4 Trigonometric Functions 22 2.2.5 Complex Numbers* 23 2.2.6 Special Mathematical Functions 25 2.3 Some Basic R Functions 27 2.3.1 Summary Statistics 27 2.3.2 is, as, is.na, etc 29 2.3.3 factors, levels, etc 31 2.3.4 Control Programming 32 2.3.5 Other Useful Functions 34 2.3.6 Calculus* 37 2.4 Vectors and Matrices in R 38 2.4.1 Vectors 39 2.4.2 Matrices 43 2.5 Data Entering and Reading from Files 48 2.5.1 Data Entering 48 2.5.2 Reading Data from External Files 51 2.6 Working with Packages 52 2.7 R Session Management 54 2.8 Bibliography 54 2.9 Complements, Problems, and Programs 55 3 Data Preparation and Other Tricks 57 3.1 Introduction 57 3.2 Manipulation with Complex Format Files 58 3.3 Reading Datasets of Foreign Formats 64 3.4 Displaying R Objects 65 3.5 Manipulation Using R Functions 66 3.6 Working with Time and Date 68 3.7 Text Manipulations 71 3.8 Scripts and Text Editors for R 73 3.8.1 Text Editors for Linuxians 74 3.9 Bibliography 75 3.10 Complements, Problems, and Programs 75 4 Exploratory Data Analysis 77 4.1 Introduction: The Tukey’s School of Statistics 77 4.2 Essential Summaries of EDA 78 4.3 Graphical Techniques in EDA 81 4.3.1 Boxplot 81 4.3.2 Histogram 86 4.3.3 Histogram Extensions and the Rootogram 90 4.3.4 Pareto Chart 93 4.3.5 Stem-and-Leaf Plot 95 4.3.6 Run Chart 100 4.3.7 Scatter Plot 101 4.4 Quantitative Techniques in EDA 103 4.4.1 Trimean 104 4.4.2 Letter Values 105 4.5 Exploratory Regression Models 107 4.5.1 Resistant Line 108 4.5.2 Median Polish 110 4.6 Bibliography 113 4.7 Complements, Problems, and Programs 114 II Probability and Inference 116 5 Probability Theory 117 5.1 Introduction 117 5.2 Sample Space, Set Algebra, and Elementary Probability 118 5.3 Counting Methods 127 5.3.1 Sampling: The DiverseWays 128 5.3.2 The Binomial Coefficients and the Pascals Triangle 132 5.3.3 Some Problems Based on Combinatorics 133 5.4 Probability: A Definition 137 5.4.1 The Prerequisites 137 5.4.2 The Kolmogorov Definition 142 5.5 Conditional Probability and Independence 146 5.6 Bayes Formula 147 5.7 Random Variables, Expectations, and Moments 149 5.7.1 The Definition 149 5.7.2 Expectation of Random Variables 153 5.8 Distribution Function, Characteristic Function, and Moment Generation Function 159 5.9 Inequalities 162 5.9.1 The Markov Inequality 162 5.9.2 The Jensen’s Inequality 163 5.9.3 The Chebyshev Inequality 163 5.10 Convergence of Random Variables 164 5.10.1 Convergence in Distributions 165 5.10.2 Convergence in Probability 167 5.10.3 Convergence in rth Mean 168 5.10.4 Almost Sure Convergence 169 5.11 The Law of Large Numbers 170 5.11.1 The Weak Law of Large Numbers 170 5.12 The Central Limit Theorem 172 5.12.1 The de Moivre–Laplace Central Limit Theorem 172 5.12.2 CLT for iid Case 173 5.12.3 The Lindeberg-Feller CLT 175 5.12.4 The Liapounov CLT 181 5.13 Bibliography 184 5.13.1 Intuitive, Elementary, and First Course Source 184 5.13.2 The Classics and Second Course Source 184 5.13.3 The Problem Books 185 5.13.4 Other Useful Source 185 5.13.5 R for Probability 185 5.14 Complements, Problems, and Programs 186 6 Probability and Sampling Distributions 188 6.1 Introduction 188 6.2 Discrete Univariate Distributions 189 6.2.1 The Discrete Uniform Distribution 189 6.2.2 The Binomial Distribution 190 6.2.3 The Geometric Distribution 193 6.2.4 The Negative Binomial Distribution 195 6.2.5 Poisson Distribution 197 6.2.6 The Hypergeometric Distribution 200 6.3 Continuous Univariate Distributions 201 6.3.1 The Uniform Distribution 201 6.3.2 The Beta Distribution 204 6.3.3 The Exponential Distribution 205 6.3.4 The Gamma Distribution 206 6.3.5 The Normal Distribution 207 6.3.6 The Cauchy Distribution 210 6.3.7 The t-Distribution 211 6.3.8 The Chi-square Distribution 211 6.3.9 The F-Distribution 212 6.4 Multivariate Probability Distributions 212 6.4.1 The Multinomial Distribution 213 6.4.2 Dirichlet Distribution 213 6.4.3 The Multivariate Normal Distribution 214 6.4.4 The Multivariate t Distribution 214 6.5 Populations and Samples 215 6.6 Sampling from the Normal Distributions 216 6.7 Some Finer Aspects of Sampling Distributions 219 6.7.1 Sampling Distribution of Median 219 6.7.2 Sampling Distribution of Mean of Standard Distributions 221 6.8 Multivariate Sampling Distributions 222 6.8.1 Noncentral Univariate Chi-square, t, and F Distributions223 6.8.2 Wishart Distribution 225 6.8.3 Hotellings T2 Distribution 226 6.9 Bayesian Sampling Distributions 226 6.10 Bibliography 228 6.11 Complements, Problems, and Programs 228 7 Parametric Inference 230 7.1 Introduction 230 7.2 Families of Distribution 232 7.2.1 The Exponential Family 234 7.2.2 Pitman Family 235 7.3 Loss Functions 236 7.4 Data Reduction 239 7.4.1 Sufficiency 239 7.4.2 Minimal Sufficiency 242 7.5 Likelihood and Information 244 7.5.1 The Likelihood Principle 244 7.5.2 The Fisher Information 250 7.6 Point Estimation 255 7.6.1 Maximum Likelihood Estimation 255 7.6.2 Method of Moments Estimator 264 7.7 Comparison of Estimators 266 7.7.1 Unbiased Estimators 266 7.7.2 Improving Unbiased Estimators 269 7.8 Confidence Intervals 271 7.9 Testing Statistical Hypotheses - The Preliminaries 272 7.10 The Neyman-Pearson Lemma 277 7.11 Uniformly Most Powerful Tests 283 7.12 Uniformly Most Powerful Unbiased Tests 288 7.12.1 Tests for the Means: One- and Two- Sample t-Test 291 7.13 Likelihood Ratio Tests 293 7.13.1 Normal Distribution: One-Sample Problems 294 7.13.2 Normal Distribution: Two-Sample Problem for the Mean297 7.14 Behrens-Fisher Problem 298 7.15 Multiple Comparison Tests 300 7.15.1 Bonferroni’s Method 301 7.15.2 Holm’s Method 302 7.16 The EM Algorithm * 303 7.16.1 Introduction 303 7.16.2 The Algorithm 304 7.16.
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons, Inc
• Publication Date: 2016
• Extent: 1 online resource
• Subjects: 519.50285511; Mathematical statistics -- Data processing; R (Computer program language)
• Languages: English
• ISBNs: 9781119152750; 9781119152736
• Related ISBNs: 9781119152729
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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