Advanced Statistics with Applications in R

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.

Auteur

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.

Texte du rabat
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 ??? 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/6;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. "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

Résumé
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 ? 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.

Contenu

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…