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R Language Features: Analytics

Features of the R language for Mathematics and Statistics

*** Requires additional open-source community packages from CRAN

Basic Mathematics

  • Complex arithmetic
  • Computation of orthogonal polynomials
  • Cross products
  • Cumulative products and sums
  • Exponential functions
  • Hyperbolic functions
  • Kronecker products on arrays
  • Logarithms (any base)
  • Logical operators
  • Matrix operations including
    • median polish of a matrix
    • QR decomposition
    • singular value decomposition
    • spectral decomposition
  • Symbolic and algorithmic derivatives
  • Trigonometric functions

Basic Statistics

  • mean
  • standard deviation
  • variance
  • median
  • quantile
  • correlation
  • cross tabulations

Probability Distributions

Density, quantiles, probability and simulation for:

  • Beta
  • Binomial
  • Birthday
  • Chi-squared
  • Empirical cumulative distribution
  • Exponential
  • F Distribution
  • Gamma
  • Geometric
  • Logistic
  • Lognormal
  • Negative Binomial
  • Normal
  • Poisson
  • Student's t
  • Tukey's studentized range distribution
  • Uniform
  • Weibull
  • Wilcoxon signed rank distribution
  • Wilcoxon rank sum distribution

Machine Learning

  • Cluster Analysis
    • K-means
    • Hierarchical clustering
  • General tree structures
  • Neural Networks
  • Trees and Recursive Partitioning

Optimization and Mathematical Programming

  • General purpose optimization
  • Linear constrained optimization
  • Linear programming
  • Nonlinear programming
  • One dimensional optimization
  • Optimization using PORT routines

Signal Processing

  • Convolutions
  • Fast Discrete Fourier Transform
  • FFT
  • Filters
  • Holt-Winter filtering
  • Kalman Filtering
  • Wavelets***

Simulation and Random Number Generation

  • The default RNG is the Mersenne-Twister algorithm.
  • Other generators include
    • Wichmann-Hill
    • Marsaglia-Multicarry
    • Super-Duper
    • Knuth-TAOCP
    • Knuth-TAOCP-2002, as well as
    • user-supplied RNGs.
  • normal random number algorithms :
    • Kinderman-Ramage
    • Ahrens-Dieter
    • Box-Muller
    • Inversion (default).
  • Pseudo-randomness:
  • Quasi-random sequences randtoolbox ***
    • the Sobol sequence
    • the Halton (hence Van Der Corput) sequence
    • the Torus sequence (also known as Kronecker sequence).
    • latin hypercube sampling lhs ***
    • quasi/pseudo random method mc2d ***
  • True randomness: random conectionn to random.org .***
  • RNG tests: RDieHarder ***

Statistical Modeling

  • Analysis of Variance (ANOVA)
  • Factor Analysis
  • Design of Experiments (DoE) & Analysis of Experimental Data
  • Kernel density estimation
  • Linear Models
    • Linear Regression
    • Multiple Regression
    • Comparison of linear models
    • Gaussian mixed-effect models
    • Generalized Additive Models *** mgvc
    • Generalized Linear Models (GLM)
    • GLM ANOVA stats
    • Hierarchical and mixed effects models
  • Multivariate Statistics
    • Multidimensional scaling
    • Multivariate ANOVA
  • Non-linear models
    • Gaussian mixed-effect models
    • Non-linear least squares
  • Principal Components Analysis
  • Robust Statistical Methods
  • Spatial statistics
  • Survival Analysis
  • Time Series Analysis
    • Autoregressive models
    • ARIMA models
      • SARIMA
      • ARIMAX
      • Subset ARIMA models
    • ARCH and GARCH models***
    • Classical decomposition
    • Embedded time series
    • Exponential smoothing models
    • Holt-Winters forecasting
    • Moving Average models
    • Spectral Analysis
    • Vector Autoregressive models (VAR)

Statistical Tests

  • Bartlett test of homogeneity of variances
  • Box-Pierce and Lyjung-Box tests
  • Cochran-Mantel-Haenszel Chi-Squared Test for Count Data
  • F test to compare two variances
  • Fisher's Exact test for count data
  • Kolmogorov-Smirnov test
  • Kruskal-Wallis Rank Sum test
  • Mood Two-Sample Test of Scale
  • Pairwise t tests
  • Pairwise Wilcoxon Rank Sum tests
  • Power calculations for 1 and 2 sample t tests
  • Shapiro-Wilk Normality test
  • Student's t-test
  • Tukey Honest Significant Differences
  • Wilcoxon Rank Sum and Signed Tess

 

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