Mathematical Statistics with Applications in R 3rd edition by Kandethody Ramachandran, Chris Tsokos – Ebook PDF Instant Download/Delivery: 0128178164, 9780128178164
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ISBN 10: 0128178164
ISBN 13: 9780128178164
Author: Kandethody Ramachandran, Chris Tsokos
Mathematical Statistics with Applications in R, Third Edition, offers a modern calculus-based theoretical introduction to mathematical statistics and applications. The book covers many modern statistical computational and simulation concepts that are not covered in other texts, such as the Jackknife, bootstrap methods, the EM algorithms, and Markov chain Monte Carlo (MCMC) methods, such as the Metropolis algorithm, Metropolis-Hastings algorithm and the Gibbs sampler. By combining discussion on the theory of statistics with a wealth of real-world applications, the book helps students to approach statistical problem-solving in a logical manner. Step-by-step procedure to solve real problems make the topics very accessible.
- Presents step-by-step procedures to solve real problems, making each topic more accessible
- Provides updated application exercises in each chapter, blending theory and modern methods with the use of R
- Includes new chapters on Categorical Data Analysis and Extreme Value Theory with Applications
- Wide array coverage of ANOVA, Nonparametric, Bayesian and empirical methods
Mathematical Statistics with Applications in R 3rd Table of contents:
1 – Descriptive statistics
1.1 Introduction
1.1.1 Data collection
1.2 Basic concepts
1.2.1 Types of data
Exercises 1.2
1.3 Sampling schemes
1.3.1 Errors in sample data
1.3.2 Sample size
Exercises 1.3
1.4 Graphical representation of data
Exercises 1.4
1.5 Numerical description of data
1.5.1 Numerical measures for grouped data
1.5.2 Box plots
Exercises 1.5
1.6 Computers and statistics
1.7 Chapter summary
1.8 Computer examples
1.8.1 R introduction and examples
Importing a CSV file
Exporting a CSV
1.8.2 Minitab examples
1.8.3 SPSS examples
1.8.4 SAS examples
Exercises 1.8
Projects for chapter 1
1A World Wide Web and data collection
1B Preparing a list of useful Internet sites
1C Dot plots and descriptive statistics
1D Importance of statistics in our society
1E Uses and misuses of statistics
2 – Basic concepts from probability theory
2.1 Introduction
2.2 Random events and probability
Exercises 2.2
2.3 Counting techniques and calculation of probabilities
Exercises 2.3
2.4 The conditional probability, independence, and Bayes’ rule
Exercises 2.4
2.5 Random variables and probability distributions
Exercises 2.5
2.6 Moments and moment-generating functions
2.6.1 Skewness and kurtosis
Exercises 2.6
2.7 Chapter summary
2.8 Computer examples (optional)
2.8.1 Examples using R
2.8.2 Minitab computations
2.8.3 SPSS examples
2.8.4 SAS examples
Projects for chapter 2
2A The birthday problem
2B The Hardy-Weinberg law
2C Some basic probability simulation
3 – Additional topics in probability
3.1 Introduction
3.2 Special distribution functions
3.2.1 The binomial probability distribution
3.2.2 Poisson probability distribution
3.2.3 Uniform probability distribution
3.2.4 Normal probability distribution
3.2.5 Gamma probability distribution
Exercises 3.2
3.3 Joint probability distributions
3.3.1 Covariance and correlation
Exercises 3.3
3.4 Functions of random variables
3.4.1 Method of distribution functions
3.4.2 The probability density function of Y = g(X), where g is differentiable and monotone increasin
3.4.3 Probability integral transformation
3.4.4 Functions of several random variables: method of distribution functions
3.4.5 Transformation method
Exercises 3.4
3.5 Limit theorems
Exercises 3.5
3.6 Chapter summary
3.7 Computer examples (optional)
3.7.1 The R examples
3.7.2 Minitab examples
3.7.3 Distribution checking
3.7.4 SPSS examples
3.7.5 SAS examples
Projects for Chapter 3
3A Mixture distribution
3B Generating samples from exponential and Poisson probability distribution
Exercise 3B
3C Coupon collector’s problem
3D Recursive calculation of binomial and Poisson probabilities
3E Simulation of Poisson approximation of binomial
3F Generating a large amount of random data using R
4 – Sampling distributions
4.1 Introduction
4.1.1 Finite populations
Exercises 4.1
4.2 Sampling distributions associated with normal populations
4.2.1 Chi-square distribution
4.2.2 Student t distribution
4.2.3 F-distribution
Exercises 4.2
4.3 Order statistics
Exercises 4.3
4.4 The normal approximation to the binomial distribution
Exercises 4.4
4.5 Chapter summary
4.6 Computer examples
4.6.1 Examples using R
4.6.2 Minitab examples
4.6.3 SPSS examples
4.6.4 SAS examples
Projects for chapter 4
4A A method to obtain random samples from different distributions
4B Simulation experiments
4C A test for normality
Exercises
5 – Statistical estimation
5.1 Introduction
5.2 The methods of finding point estimators
5.2.1 The method of moments
5.2.2 The method of maximum likelihood
5.2.2.1 Some additional probability distributions
Exercises 5.2
5.3 Some desirable properties of point estimators
5.3.1 Unbiased estimators
5.3.2 Sufficiency
Exercises 5.3
5.4 A method of finding the confidence interval: pivotal method
Exercises 5.4
5.5 One-sample confidence intervals
5.5.1 Large-sample confidence intervals
5.5.2 Confidence interval for proportion, p
5.5.2.1 Margin of error and sample size
5.5.3 Small-sample confidence intervals for μ
Exercises 5.5
5.6 A confidence interval for the population variance
Exercises 5.6
5.7 Confidence interval concerning two population parameters
Exercises 5.7
5.8 Chapter summary
5.9 Computer examples
5.9.1 Examples using R
5.9.2 Minitab examples
5.9.3 SPSS examples
5.9.4 SAS examples
Exercises 5.9
5.10 Projects for Chapter 5
5.10.1 Asymptotic properties
5.10.2 Robust estimation
5.10.3 Numerical unbiasedness and consistency
5.10.4 Averaged squared errors
5.10.5 Alternate method of estimating the mean and variance
5.10.6 Newton-Raphson in one dimension
5.10.7 The empirical distribution function
5.10.8 Simulation of coverage of the small confidence intervals for μ
5.10.9 Confidence intervals based on sampling distributions
5.10.10 Large-sample confidence intervals: general case
5.10.11 Prediction interval for an observation from a normal population
5.10.12 Empirical distribution function as estimator for cumulative distribution function
6 – Hypothesis testing
6.1 Introduction
6.1.1 Sample size
Exercises 6.1
6.2 The Neyman-Pearson lemma
Exercises 6.2
6.3 Likelihood ratio tests
Exercises 6.3
6.4 Hypotheses for a single parameter
6.4.1 The p value
6.4.2 Hypothesis testing for a single parameter
Exercises 6.4
6.5 Testing of hypotheses for two samples
6.5.1 Independent samples
6.5.1.1 Equal variances
6.5.1.2 Unequal variances: Welch’s t-test (σ12≠σ22)
6.5.2 Dependent samples
Exercises 6.5
6.6 Chapter summary
6.7 Computer examples
6.7.1 R examples
6.7.2 Minitab examples
6.7.3 SPSS examples
6.7.4 SAS examples
Projects for Chapter 6
6A Testing on computer-generated samples
6B Conducting a statistical test with confidence interval
7 – Linear regression models
7.1 Introduction
7.2 The simple linear regression model
7.2.1 The method of least squares
7.2.2 Derivation of β^0 and β^1
7.2.3 Quality of the regression
7.2.4 Properties of the least-squares estimators for the model Y=β0 + β1x + ε
7.2.5 Estimation of error variance σ2
Exercises 7.2
7.3 Inferences on the least-squares estimators
7.3.1 Analysis of variance approach to regression
Exercises 7.3
7.4 Predicting a particular value of Y
Exercises 7.4
7.5 Correlation analysis
Exercises 7.5
7.6 Matrix notation for linear regression
7.6.1 ANOVA for multiple regression
Exercises 7.6
7.7 Regression diagnostics
7.8 Chapter summary
7.9 Computer examples
7.9.1 Examples using R
7.9.2 Minitab examples
7.9.3 SPSS examples
7.9.4 SAS examples
Projects for chapter 7
7A Checking the adequacy of the model by scatterplots
7B The coefficient of determination
7C Outliers and high leverage points
8 – Design of experiments
8.1 Introduction
8.2 Concepts from experimental design
8.2.1 Basic terminology
8.2.2 Fundamental principles: replication, randomization, and blocking
8.2.3 Some specific designs
Exercises 8.2
8.3 Factorial design
8.3.1 One-factor-at-a-time design
8.3.2 Full factorial design
8.3.3 Fractional factorial design
Exercises 8.3
8.4 Optimal design
8.4.1 Choice of optimal sample size
Exercises 8.4
8.5 The Taguchi methods
Exercises 8.5
8.6 Chapter summary
8.7 Computer examples
8.7.1 Examples using R
8.7.2 Minitab examples
8.7.3 SAS examples
Projects for chapter 8
8A Sample size and power
8B Effect of temperature on the spoilage of milk
9 – Analysis of variance
9.1 Introduction
9.2 Analysis of variance method for two treatments (optional)
Exercises 9.2
9.3 Analysis of variance for a completely randomized design
9.3.1 The p-value approach
9.3.2 Testing the assumptions for one-way analysis of variance
9.3.3 Model for one-way analysis of variance (optional)
Exercises 9.3
9.4 Two-way analysis of variance, randomized complete block design
Exercises 9.4
9.5 Multiple comparisons
Exercises 9.5
9.6 Chapter summary
9.7 Computer examples
9.7.1 Examples using R
9.7.2 Minitab examples
9.7.3 SPSS examples
9.7.4 SAS examples
Exercises 9.7
Projects for Chapter 9
9A Transformations
9B Analysis of variance with missing observations
9C Analysis of variance in linear models
10 – Bayesian estimation and inference
10.1 Introduction
10.2 Bayesian point estimation
10.2.1 Criteria for finding the Bayesian estimate
Exercises 10.2
10.3 Bayesian confidence interval or credible interval
Exercises 10.3
10.4 Bayesian hypothesis testing
Exercises 10.4
10.5 Bayesian decision theory
Exercises 10.5
10.6 Empirical Bayes estimates
10.6.1 Jackknife resampling
10.6.2 Bootstrap resampling
10.6.3 Parametric, standard Bayes, empirical Bayes: Bootstrapping and jackknife
Exercises 10.6
10.7 Chapter summary
10.8 Computer examples
10.8.1 Examples with R
Project for Chapter 10
10A Predicting future observations
11 – Categorical data analysis and goodness-of-fit tests and applications
11.1 Introduction
11.2 Contingency tables and probability calculations
Exercises 11.2
11.3 Estimation in categorical data
11.3.1 Large sample confidence intervals for p
11.4 Hypothesis testing in categorical data analysis
11.4.1 The chi-square tests for count data: one-way analysis
11.4.2 Two-way contingency table: test for independence
Exercises 11.4
11.5 Goodness-of-fit tests to identify the probability distribution
11.5.1 Pearson’s chi-square test
11.5.2 The Kolmogorov-Smirnov test: (one population)
11.5.3 The Anderson-Darling test
11.5.4 Shapiro-Wilk normality test
11.5.5 The P-P plots and Q-Q plots
11.5.5.1 Steps to construct the P-P plot
Exercises 11.5
11.6 Chapter summary
11.7 Computer examples
11.7.1 R-commands
11.7.2 Minitab examples
11.7.2.1 Chi-square test
Projects for Chapter 11
11A Fitting a distribution to data
11B Simpson’s paradox
12 – Nonparametric Statistics
12.1 Introduction
12.2 Nonparametric confidence interval
Exercises 12.2
12.3 Nonparametric hypothesis tests for one sample
12.3.1 The sign test
12.3.2 Wilcoxon signed rank test
12.3.3 Dependent samples: paired comparison tests
Exercises 12.3
12.4 Nonparametric hypothesis tests for two independent samples
12.4.1 Median test
12.4.2 The Wilcoxon rank sum test
Exercises 12.4
12.5 Nonparametric hypothesis tests for k ≥ 2 samples
12.5.1 The Kruskal-Wallis test
12.5.2 The Friedman test
Exercises 12.5
12.6 Chapter summary
12.7 Computer examples
12.7.1 Examples using R
12.7.2 Minitab examples
12.7.3 SPSS examples
12.7.4 SAS examples
Projects for Chapter 12
12A Comparison of Wilcoxon tests with normal approximation
12B Randomness test (Wald-Wolfowitz test)
Exercise
13 – Empirical methods
13.1 Introduction
13.2 The jackknife method
Exercises 13.2
13.3 An introduction to bootstrap methods
13.3.1 Bootstrap confidence intervals
Exercises 13.3
13.4 The expectation maximization algorithm
Exercises 13.4
13.5 Introduction to Markov chain Monte Carlo
13.5.1 Metropolis algorithm
13.5.2 The Metropolis-Hastings algorithm
13.5.3 Gibbs algorithm
13.5.4 Markov chain Monte Carlo issues
Exercises 13.5
13.6 Chapter summary
13.7 Computer examples
13.7.1 Examples using R
13.7.2 Examples with Minitab
13.7.3 SAS examples
Project for Chapter 13
13A Bootstrap computation
14 – Some issues in statistical applications: an overview
14.1 Introduction
14.2 Graphical methods
Exercises 14.2
14.3 Outliers
Exercises 14.3
14.4 Checking the assumptions
14.4.1 Checking the assumption of normality
14.4.2 Data transformation
14.4.3 Test for equality of variances
14.4.3.1 Testing equality of variances for two normal populations
14.4.3.2 Test for equality of variances, k≥2 populations
14.4.4 Test of independence
Exercises 14.4
14.5 Modeling issues
14.5.1 A simple model for univariate data
14.5.2 Modeling bivariate data
Exercises 14.5
14.6 Parametric versus nonparametric analysis
Exercises 14.6
14.7 Tying it all together
Exercises 14.7
14.8 Some real-world problems: applications
14.8.1 Global warming
14.8.2 Hurricane Katrina
14.8.3 National unemployment
14.8.4 Brain cancer
14.8.5 Rainfall data analysis
14.8.6 Prostate cancer
14.8 Exercises
14.9. Conclusion
I – Set theory
II – Review of Markov chains
III – Common probability distributions
IV – What is R?
V – Probability tables
References
Index
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Tags: Kandethody Ramachandran, Chris Tsokos, Mathematical Statistics, Applications in R