Eugene Demidenko

Advanced Statistics with Applications in R (eBook, PDF)

• Format: PDF

Produktbeschreibung

Advanced Statistics with Applications in R fills the gap between several excellent theoretical statistics textbooks and many applied statistics books where teaching reduces to using existing packages. This book looks at what is under the hood. Many statistics issues including the recent crisis with p-value are caused by misunderstanding of statistical concepts due to poor theoretical background of practitioners and applied statisticians. This book is the product of a forty-year experience in teaching of probability and statistics and their applications for solving real-life problems. There are more than 442 examples in the book: basically every probability or statistics concept is illustrated with an example accompanied with an R code. Many examples, such as Who said pi? What team is better? The fall of the Roman empire, James Bond chase problem, Black Friday shopping, Free fall equation: Aristotle or Galilei, and many others are intriguing. These examples cover biostatistics, finance, physics and engineering, text and image analysis, epidemiology, spatial statistics, sociology, etc. Advanced Statistics with Applications in R teaches students to use theory for solving real-life problems through computations: there are about 500 R codes and 100 datasets. These data can be freely downloaded from the author's website dartmouth.edu/~eugened. This book is suitable as a text for senior undergraduate students with major in statistics or data science or graduate students. Many researchers who apply statistics on the regular basis find explanation of many fundamental concepts from the theoretical perspective illustrated by concrete real-world applications.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 880
• Erscheinungstermin: 19. November 2019
• Englisch
• ISBN-13: 9781118594131
• Artikelnr.: 58421351

Autorenporträt

PROFESSOR EUGENE DEMIDENKO works at Dartmouth College in the Department of Biomedical Science, he teaches statistics at Mathematics Department to undergraduate students and to graduate students at Quantitative Biomedical Sciences at Geisel School of Medicine. He has brought experience in theoretical and applied statistics, such as epidemiology and biostatistics, statistical analysis of images, tumor regrowth, ill-posed inverse problems in engineering and technology, optimal portfolio allocation, among others. His first book with Wiley Mixed Model: Theory and Applications with R gained much popularity among researchers and graduate/PhD students. Prof. Demidenko is the author of a controversial paper The P-value You Can't Buy published in 2016 in The American Statistician.

Inhaltsangabe

Why I Wrote This Book

1 Discrete random variables 1

1.1 Motivating example 1

1.2 Bernoulli random variable 2

1.3 General discrete random variable 4

1.4 Mean and variance 6

1.4.1 Mechanical interpretation of the mean 7

1.4.2 Variance 12

1.5 R basics 15

1.5.1 Scripts/functions 16

1.5.2 Text editing in R 17

1.5.3 Saving your R code 18

1.5.4 for loop 18

1.5.5 Vectorized computations 19

1.5.6 Graphics 23

1.5.7 Coding and help in R 25

1.6 Binomial distribution 26

1.7 Poisson distribution 32

1.8 Random number generation using sample 38

1.8.1 Generation of a discrete random variable 38

1.8.2 Random Sudoku 39

2 Continuous random variables 43

2.1 Distribution and density functions 43

2.1.1 Cumulative distribution function 43

2.1.2 Empirical cdf 45

2.1.3 Density function 46

2.2 Mean, variance, and other moments 48

2.2.1 Quantiles, quartiles, and the median 54

2.2.2 The tight confidence range 55

2.3 Uniform distribution 59

2.4 Exponential distribution 63

2.4.1 Laplace or double-exponential distribution 67

2.4.2 R functions 67

2.5 Moment generating function 69

2.5.1 Fourier transform and characteristic function 72

2.6 Gamma distribution 75

2.6.1 Relationship to Poisson distribution 77

2.6.2 Computing the gamma distribution in R 79

2.6.3 The tight confidence range 79

2.7 Normal distribution 82

2.8 Chebyshev's inequality 91

2.9 The law of large numbers 93

2.9.1 Four types of stochastic convergence 94

2.9.2 Integral approximation using simulations 99

2.10 The central limit theorem 104

2.10.1 Why the normal distribution is the most natural symmetric distribution 112

2.10.2 CLT on the relative scale 113

2.11 Lognormal distribution 116

2.11.1 Computation of the tight confidence range 118

2.12 Transformations and the delta method 120

2.12.1 The delta method 124

2.13 Random number generation 126

2.13.1 Cauchy distribution 130

2.14 Beta distribution 132

2.15 Entropy 134

2.16 Benford's law: the distribution of the first digit 138

2.16.1 Distributions that almost obey Benford's law 142

2.17 The Pearson family of distributions 145

2.18 Major univariate continuous distributions 147

3 Multivariate random variables 149

3.1 Joint cdf and density 149

3.1.1 Expectation 154

3.1.2 Bivariate discrete distribution 154

3.2 Independence 156

3.2.1 Convolution 159

3.3 Conditional density 168

3.3.1 Conditional mean and variance 171

3.3.2 Mixture distribution and Bayesian statistics 179

3.3.3 Random sum 182

3.3.4 Cancer tumors grow exponentially 184

3.4 Correlation and linear regression 189

3.5 Bivariate normal distribution 198

3.5.1 Regression as conditional mean 206

3.5.2 Variance decomposition and coefficient of determination 208

3.5.3 Generation of dependent normal observations 209

3.5.4 Copula 214

3.6 Joint density upon transformation 218

3.7 Geometric probability 223

3.7.1 Meeting problem 224

3.7.2 Random objects on the square 225

3.8 Optimal portfolio allocation 230

3.8.1 Stocks do not correlate 231

3.8.2 Correlate

Rezensionen

"This book is superior to the current available books on market in many aspects."

--Yi Zhao, Department of Biostatistics, Johns Hopkins Bloomberg School of Public Health and Yizhen Xu, Department of biostatistics, Brown University

"This text is an excellent book suitable for a wide variety of audiences trying to learn probability, statistics, and R programming language."

--Fenghai Duan, Department of Biostatistics and Center for Statistical Sciences, Brown University School of Public Health, Providence, Rhode Island