 ## The R package

R, closely related to the commercial package S-Plus, is the largest and most comprehensive public domain statistical computing environment.  It provides a coherent, flexible programming environment for data analysis, applied mathematics, statistical analysis, and graphics.  Unlike some menu-drived statistical packages, the user interacts with R with a C-like command language with pop-up graphical windows.  The core R package is enhanced by several hundred user-supplied add-on packages in the Comprehensive R Archive Network (CRAN) and the Omegahat Project for Statistical Computing. Binary executables and open source codes for Linux, Windows and MacOS can be downloaded for instant use.  R has extensive documentation. Here we list some of its capabilities that may be of interest to the physical scientist.

### The base R package includes:

• arithmetic (scalar/vector/array)
• bootstrap resampling and confidence intervals (basic, ABC, percentile, studentized, tilted, jackknife)
• correlation coefficients (Pearson, Kendall, Spearman)
• distributions (Gaussian, Poisson, and many other statistical distributions and special functions, including random deviates)
• empirical distribution tests (Anderson-Darling, Cramer-von Mises, Kolmogorov-Smirnov) and quantiles
• exploratory data analysis
• generalized linear & generalized additive modelling
• graphics, publication-quality (scatter, dendrograms, lattice, etc)
• integration and interpolation
• linear algebra and equation solutions (extensive methods)
• linear mixed-effects modelling
• linear modelling (including nonlinear functions), resistant regression. robust M-estimators
• linear & quadratic programming (simplex, penalized constraints)
• local and ridge regression (loess, variograms)
• maximum likelihood estimation (AIC, BIC)
• multivariate analysis (tabulations, ANOVA, discriminant, factor, principal components, Mahalanobis distances, MANOVA, principal components)
• multivariate cluster analyses (agglomerative and divisive clustering, dissimilarity matrix, fuzzy, k-nearest neighbor, k-means & m-medioid partitioning, monothetic,  recursive partitioning, regression trees, self-organizing maps)
• neural networks (censored, least-squares, entropy, log-linear, maximum likelihood, perceptron)
• nonlinear least-squares regression
• smoothing (cross-validation, histograms, kernel, local regression, variogram)
• sorting
• spatial analysis & point processes (correlogram, kriging, Moran's I, Geary's C, pattern analysis, polynomial surface, simulation, variogram)
• splines (B-spline, periodic, polynomial)
• statistical tests, parametric & nonparametric (Ansari, Bartlett, binomial, Box, F, Fisher, Fligner, Friedman, Mantel-Haenzel, Mauchley, McNemar, Mood, proportions, Shapiro, t, Wilcoxon, signed rank),
• survival analysis for censored data (Cox regression, Kaplan-Meier & Fleming-Harrington survival curves, life table, linear regression, ridge regression, tobit modelling, Weibull & other survival curve fitting, k-sample tests)
• time series analysis (ARMA, acf, Box-Jenkins, FFT, Kalman filter, lags, mixed-effects, prediction, smoothing, spectral analysis)

### CRAN add-on packages treat:

(see Chapter 5 for brief individual descriptions)

• ARIMA modeling
• Bayesian computation (empirical Bayes, MCMC calculations & diagnostics, survival regression, logit/probit, networks
• Boolean hypotheses
• boosting
• bootstrap modelling
• classification and regression trees
• convex clustering & convex hulls
• conditional inference
• combinatorics
• elliptical confidence regions
• energy statistical tests
• extreme value distribution
• fixed point clusters
• genetic algorithms
• geostatistical modelling
• GUIs (Rcmdr, SciViews)
• heteroscedastic t-regression
• hidden Markov models
• hierarchical partitioning & clustering
• independent component analysis
• interpolation
• irregular time series.
• kernel smoothing
• kernel-based machine learning
• k-nearest neighbor tree classifier
• Kolmogorov-Zurbenko adaptive filtering
• least-angle and lasso regression
• linear programming (simplex)
• likelihood ratios
• local regression density estimators
• logistic regression
• map projections
• Matlab emulator
• matrices, sparse matrices, tensor decomposition
• Markov chain Monte Carlo
• mixture models
• mixture discriminant analysis
• model-based clustering
• nonlinear least squares
• Markov multistate models
• mixture models & regression
• multidimensional analysis
• multimodality test
• multivariate time series
• multivariate Shapiro-Wilk test
• multivariate outlier detection
• multivariate normal partitioning
• multivariate normals with missing data
• neural networks
• non-linear time series analysis
• nonparametric multiple comparisons
• omnibus tests for normality
• orientation data, outlier detection
• parallel coordinates plots
• partial least squares
• periodic autoregression analysis
• Poisson-Gamma additive models
• polychoric and polyserial correlations
• principal component regression
• principal curve fits
• projection pursuit
• proportional hazards modelling
• quantile regression
• quasi-variances
• random fields
• random forest classification
• ridge regression
• robust regression
• Sampford sampling
• segmented regression break points
• self-organizing maps
• shape analysis
• space-time ecological data analysis
• spatial analysis and kriging
• spline fits & regressions (MARS, BRUTO)
• structural regression with splines
• tesselations & Delaunay trangulation
• three-dimensional visualization
• two-stage least squares regression
• unit root tests
• variogram diagnostics
• wavelet toolbox & denoising
• weighted likelihood robust inference

### CRAN includes codes and datasets associated with textbooks on:

• Bayesian statistics
• bootstrapping
• circular statistics
• contingency tables
• data analysis
• engineering statistics
• econometrics
• kernel smoothing
• generalized additive models
• image analysis
• linear regression
• relative distribution methods
• smoothing
• survival analysis (censored data)
• time-frequency analysis

### Through base R, CRAN and the Omegahat Project, R interfaces to the following languages, formats and protocols:

• Languages : BUGS, C, Fortran, Java, Python, Perl, XLisp