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# R Language Features: Analytics

*** 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*:- RNGs from GNU GSL RDieHarder ***
- SF Merseene Twister
- Well randtoolbox ***

*Quasi-random sequences*randtoolbox ****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