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Probability and Statistics with R [Kietas viršelis]

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(Public University of Navarre, Pamplona, Spain), (Appalachian State University, Boone, North Carolina, USA), (Public University of Navarre, Pamplona, Spain)
  • Formatas: Hardback, 726 pages, aukštis x plotis: 254x178 mm, weight: 1452 g, 141 Tables, black and white; 176 Illustrations, black and white
  • Išleidimo metai: 01-Apr-2008
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584888911
  • ISBN-13: 9781584888918
Kitos knygos pagal šią temą:
Probability and Statistics with RDidesnis paveikslėlis
  • Formatas: Hardback, 726 pages, aukštis x plotis: 254x178 mm, weight: 1452 g, 141 Tables, black and white; 176 Illustrations, black and white
  • Išleidimo metai: 01-Apr-2008
  • Leidėjas: Chapman & Hall/CRC
  • ISBN-10: 1584888911
  • ISBN-13: 9781584888918
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781584888918.html
Raktažodžiai:
Designed for an intermediate undergraduate course, Probability and Statistics with R shows students how to solve various statistical problems using both parametric and nonparametric techniques via the open source software R. It provides numerous real-world examples, carefully explained proofs, end-of-chapter problems, and illuminating graphs to facilitate hands-on learning. Integrating theory with practice, the text briefly introduces the syntax, structures, and functions of the S language, before covering important graphically and numerically descriptive methods. The next several chapters elucidate probability and random variables topics, including univariate and multivariate distributions. After exploring sampling distributions, the authors discuss point estimation, confidence intervals, hypothesis testing, and a wide range of nonparametric methods. With a focus on experimental design, the book also presents fixed- and random-effects models as well as randomized block and two-factor factorial designs. The final chapter describes simple and multiple regression analyses.

Demonstrating that R can be used as a powerful teaching aid, this comprehensive text presents extensive treatments of data analysis using parametric and nonparametric techniques. It effectively links statistical concepts with R procedures, enabling the application of the language to the vast world of statistics.

Recenzijos

This book covers a wide range of topics in both theoretical and applied statistics the authors list both R and SPLUS commands and clearly note when a command is applicable only in either SPLUS or R. Therefore, SPLUS users also should find this book useful. Detailed executable codes and codes to generate the figures in each chapter are available online at http://www1.appstate.edu/~arnholta/PASWR/front.htm nicely blend[ s] mathematical statistics, statistical inference, statistical methods, and computational statistics using S language ... . Students or self-learners can learn some basic techniques for using R in statistical analysis on their way to learning about various topics in probability and statistics. This book also could serve as a wonderful stand-alone textbook in probability and statistics if the computational statistics portions are skipped. 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 of statistical analysis and application that the social researcher may need in their work. I would recommend it as a useful addition to the bookshelf. Eirini Koutoumanou, University College London, Significance, December 2008

A Brief Introduction to S
1(28)
The Basics of S
1(1)
Using S
1(1)
Data Sets
2(1)
Data Manipulation
3(17)
S Structures
3(1)
Mathematical Operations
4(1)
Vectors
4(1)
Sequences
5(2)
Reading Data
7(1)
Using scan()
7(1)
Using read .table()
8(1)
Using write()
8(1)
Using dump () and source ()
9(1)
Logical Operators and Missing Values
9(3)
Matrices
12(2)
Vector and Matrix Operations
14(1)
Arrays
15(1)
Lists
16(1)
Data Frames
16(1)
Tables
17(2)
Functions Operating on Factors and Lists
19(1)
Probability Functions
20(1)
Creating Functions
21(1)
Programming Statements
22(1)
Graphs
23(2)
Problems
25(4)
Exploring Data
29(48)
What Is Statistics?
29(1)
Data
29(1)
Displaying Qualitative Data
30(3)
Tables
30(1)
Barplots
31(1)
Dot Charts
32(1)
Pie Charts
32(1)
Displaying Quantitative Data
33(6)
Stem-and-Leaf Plots
33(2)
Strip Charts (R Only)
35(1)
Histograms
36(3)
Summary Measures of Location
39(8)
The Mean
39(2)
The Median
41(1)
Quantiles
42(2)
Hinges and Five-Number Summary
44(1)
Boxplots
45(2)
Summary Measures of Spread
47(2)
Range
47(1)
Interquartile Range
47(1)
Variance
48(1)
Bivariate Data
49(16)
Two-Way Contingency Tables
49(2)
Graphical Representations of Two-Way Contingency Tables
51(2)
Comparing Samples
53(3)
Relationships between Two Numeric Variables
56(2)
Correlation
58(1)
Sorting a Data Frame by One or More of Its Columns
59(1)
Fitting Lines to Bivariate Data
60(5)
Multivariate Data (Lattice and Trellis Graphs)
65(6)
Arranging Several Graphs on a Single Page
67(2)
Panel Functions
69(2)
Problems
71(6)
General Probability and Random Variables
77(38)
Introduction
77(1)
Counting Rules
77(3)
Sampling With Replacement
77(1)
Sampling Without Replacement
78(1)
Combinations
79(1)
Probability
80(7)
Sample Space and Events
80(1)
Set Theory
80(1)
Interpreting Probability
81(1)
Relative Frequency Approach to Probability
81(1)
Axiomatic Approach to Probability
81(2)
Conditional Probability
83(1)
The Law of Total Probability and Bayes' Rule
84(2)
Independent Events
86(1)
Random Variables
87(20)
Discrete Random Variables
88(1)
Mode, Median, and Percentiles
89(1)
Expected Values of Discrete Random Variables
90(2)
Moments
92(1)
Variance
92(1)
Rules of Variance
92(1)
Continuous Random Variables
93(3)
Numerical Integration with S
96(1)
Mode, Median, and Percentiles
96(2)
Expectation of Continuous Random Variables
98(2)
Markov's Theorem and Chebyshev's Inequality
100(2)
Weak Law of Large Numbers
102(1)
Skewness
102(2)
Moment Generating Functions
104(3)
Problems
107(8)
Univariate Probability Distributions
115(56)
Introduction
115(1)
Discrete Univariate Distributions
115(15)
Discrete Uniform Distributions
115(1)
Bernoulli and Binomial Distributions
116(4)
Poisson Distribution
120(6)
Geometric Distribution
126(2)
Negative Binomial Distribution
128(1)
Hypergeometric Distribution
129(1)
Continuous Univariate Distributions
130(32)
Uniform Distribution (Continuous)
130(3)
Exponential Distribution
133(6)
Gamma Distribution
139(4)
Hazard Function, Reliability Function, and Failure Rate
143(4)
Weibull Distribution
147(2)
Beta Distribution
149(3)
Normal (Gaussian) Distribution
152(10)
Problems
162(9)
Multivariate Probability Distributions
171(26)
Joint Distribution of Two Random Variables
171(3)
Joint pdf for Two Discrete Random Variables
171(2)
Joint pdf for Two Continuous Random Variables
173(1)
Independent Random Variables
174(1)
Several Random Variables
175(2)
Conditional Distributions
177(3)
Expected Values, Covariance, and Correlation
180(5)
Expected Values
180(1)
Covariance
181(2)
Correlation
183(2)
Multinomial Distribution
185(1)
Bivariate Normal Distribution
186(4)
Problems
190(7)
Sampling and Sampling Distributions
197(29)
Sampling
197(4)
Simple Random Sampling
198(2)
Stratified Sampling
200(1)
Systematic Sampling
200(1)
Cluster Sampling
201(1)
Parameters
201(2)
Infinite Populations' Parameters
202(1)
Finite Populations' Parameters
202(1)
Estimators
203(3)
Empirical Probability Distribution Function
204(2)
Plug-In Principle
206(1)
Sampling Distribution of the Sample Mean
206(6)
Sampling Distribution for a Statistic from an Infinite Population
212(7)
Sampling Distribution for the Sample Mean
212(1)
First Case: Sampling Distribution of X when Sampling from a Normal Distribution
212(3)
Second Case: Sampling Distribution of X when X is not a Normal Random Variable
215(4)
Sampling Distribution for X---Y when Sampling from Two Independent Normal Populations
219(1)
Sampling Distribution for the Sample Proportion
220(5)
Expected Value and Variance of the Uncorrected Sample Variance and the Sample Variance
225(1)
Sampling Distributions Associated with the Normal Distribution
226(19)
Chi-Square Distribution (X2)
226(15)
The Relationship between the X2 Distribution and the Normal Distribution
228(3)
Sampling Distribution for S2u and S2 when Sampling from Normal Populations
231(4)
t-Distribution
235(3)
The F Distribution
238(3)
Problems
241(4)
Point Estimation
245(46)
Introduction
245(1)
Properties of Point Estimators
245(10)
Mean Square Error
245(2)
Unbiased Estimators
247(2)
Efficiency
249(3)
Consistent Estimators
252(2)
Robust Estimators
254(1)
Point Estimation Techniques
255(27)
Method of Moments Estimators
255(2)
Likelihood and Maximum Likelihood Estimators
257(13)
Fisher Information
270(1)
Fisher Information for Sevral Parameters
271(2)
Properties of Maximum Likelihood Estimators
273(5)
Finding Maximum Likelihood Estimators for Multiple Parameters
278(2)
Multi-Parameter Properties of MLEs
280(2)
Problems
282(9)
Confidence Intervals
291(50)
Introduction
291(1)
Confidence Intervals for Population Means
292(24)
Confidence Interval for the Population Mean when Sampling from a Normal Distribution with Known Population Variance
292(5)
Determining Required Sample Size
297(3)
Confidence Interval for the Population Mean when Sampling from a Normal Distribution with Unknown Population Variance
300(2)
Confidence Interval for the Difference in Population Means when Sampling from Independent Normal Distributions with Known Equal Variances
302(3)
Confidence Interval for the Difference in Population Means when Sampling from Independent Normal Distributions with Known but Unequal Variances
305(3)
Confidence Interval for the Difference in Means when Sampling from Independent Normal Distributions with Variances That Are Unknown but Assumed Equal
308(2)
Confidence Interval for a Difference in Means when Sampling from Independent Normal Distributions with Variances That Are Unknown and Unequal
310(3)
Confidence Interval for the Mean Difference when the Differences Have a Normal Distribution
313(3)
Confidence Intervals for Population Variances
316(5)
Confidence Interval for the Population Variance of a Normal Population
316(3)
Confidence Interval for the Ratio of Population Variances when Sampling from Independent Normal Distributions
319(2)
Confidence Intervals Based on Large Samples
321(10)
Confidence Interval for the Population Proportion
322(5)
Confidence Interval for a Difference in Population Proportions
327(2)
Confidence Interval for the Mean of a Poisson Random Variable
329(2)
Problems
331(10)
Hypothesis Testing
341(62)
Introduction
341(1)
Type I and Type II Errors
342(3)
Power Function
345(3)
Uniformly Most Powerful Test
348(2)
Value or Critical Level
350(1)
Tests of Significance
351(2)
Hypothesis Tests for Population Means
353(20)
Test for the Population Mean when Sampling from a Normal Distribution with Known Population Variance
353(2)
Test for the Population Mean when Sampling from a Normal Distribution with Unknown Population Variance
355(6)
Test for the Difference in Population Means when Sampling from Independent Normal Distributions with Known Variances
361(2)
Test for the Difference in Means when Sampling from Independent Normal Distributions with Variances that are Unknown but Assumed Equal
363(4)
Test for a Difference in Means when Sampling from Independent Normal Distributions with Variances That Are Unknown and Unequal
367(3)
Test for the Mean Difference when the Differences Have a Normal Distribution
370(3)
Hypothesis Tests for Population Variances
373(6)
Test for the Population Variance when Sampling from a Normal Distribution
373(3)
Test for Equality of Variances when Sampling from Independent Normal Distributions
376(3)
Hypothesis Tests for Population Proportions
379(17)
Testing the Proportion of Successes in a Binomial Experiment (Exact Test)
379(4)
Testing the Proportion of Successes in a Binomial Experiment (Normal Approximation)
383(4)
Testing Equality of Proportions with Fisher's Exact Test
387(5)
Large Sample Approximation for Testing the Difference of Two Proportions
392(4)
Problems
396(7)
Nonparametric Methods
403(88)
Introduction
403(1)
Sign Test
403(7)
Confidence Interval Based on the Sign Test
404(1)
Normal Approximation to the Sign Test
405(5)
Wilcoxon Signed-Rank Test
410(13)
Confidence Interval for ψ Based on the Wilcoxon Signed-Rank Test
414(4)
Normal Approximation to the Wilcoxon Signed-Rank Test
418(5)
The Wilcoxon Rank-Sum or the Mann-Whitney U-Test
423(13)
Confidence Interval Based on the Mann-Whitney U-Test
427(2)
Normal Approximation to the Wilcoxon Rank-Sum and Mann- Whitney U-Tests
429(7)
The Kruskal-Wallis Test
436(6)
Friedman Test for Randomized Block Designs
442(5)
Goodness-of-Fit Tests
447(15)
The Chi-Square Goodness-of-Fit Test
447(7)
Kolmogorov-Smirnov Goodness-of-Fit Test
454(7)
Shapiro-Wilk Normality Test
461(1)
Categorical Data Analysis
462(7)
Test of Independence
464(2)
Test of Homogeneity
466(3)
Nonparametric Bootstrapping
469(10)
Bootstrap Paradigm
469(3)
Confidence Intervals
472(7)
Permutation Tests
479(5)
Problems
484(7)
Experimental Design
491(72)
Introduction
491(4)
Fixed Effects Model
495(2)
Analysis of Variance (ANOVA)for the One-Way Fixed Effects Model
497(4)
Power and the Non-Central F Distribution
501(9)
Checking Assumptions
510(4)
Checking for Independence of Errors
510(1)
Checking for Normality of Errors
511(1)
Checking for Constant Variance
512(2)
Fixing Problems
514(4)
Non-Normality
515(1)
Non-Constant Variance
516(2)
Multiple Comparisons of Means
518(4)
Fisher's Least Significant Difference
519(1)
The Tukey's Honestly Significant Difference
520(1)
Displaying Pairwise Comparisons
521(1)
Other Comparisons among the Means
522(7)
Orthogonal Contrasts
523(6)
The Scheffe Method for All Constrasts
529(1)
Summary of Comparisons of Means
529(5)
Random Effects Model (Variance Components Model)
534(3)
Randomized Complete Block Design
537(10)
Two-Factor Factorial Design
547(9)
Problems
556(7)
Regression
563(96)
Introduction
563(2)
Simple Linear Regression
565(1)
Multiple Linear Regression
565(2)
Ordinary Least Squares
567(3)
Properties of the Fitted Regression Line
570(1)
Using Matrix Notation with Ordinary Least Squares
571(5)
The Method of Maximum Likelihood
576(1)
The Sampling Distribution of β
577(3)
ANOVA Approach to Regression
580(13)
ANOVA with Simple Linear Regression
581(3)
ANOVA with Multiple Linear Regression
584(2)
Coefficient of Determination
586(1)
Extra Sum of Squares
587(2)
Tests on a Single Parameter
589(2)
Tests on Subsets of the Regression Parameters
591(2)
General Linear Hypothesis
593(4)
Model Selection and Validation
597(33)
Testing-Based Procedures
597(1)
Backward Elimination
597(1)
Forward Selection
597(1)
Stepwise Regression
598(1)
Criterion-Based Procedures
598(8)
Summary
606(1)
Diagnostics
607(1)
Checking Error Assumptions
607(1)
Assessing Normality and Constant Variance
608(1)
Testing Autocorrelation
609(1)
Identifying Unusual Observations
610(3)
High Leverage Observations
613(7)
Transformations
620(3)
Collinearity
623(3)
Transformations for Non-Normality and Unequal Error Variances
626(4)
Interpreting a Logarithmically Transformed Model
630(2)
Qualitative Predictors
632(6)
Estimation of the Mean Response for New Values Xh
638(1)
Prediction and Sampling Distribution of New Observations Yh(new)
639(3)
Simultaneous Confidence Intervals
642(6)
Simultaneous Confidence Intervals for Several Mean Responses --- Confidence Band
642(1)
Predictions of g New Obsevations
643(1)
Distinguishing Pointwise Confidence Envelopes from Confidence Bands
643(5)
Problems
648(11)
A S Commands
659(12)
B Quadratic Forms and Random Vectors and Matrices
671(4)
B.1 Quadratic Forms
671(1)
B.2 Random Vectors and Matrices
672(1)
B.3 Variance of Random Vectors
672(3)
References 675(8)
Index 683