Statistics Library Features
Below is a list of features for the statistics library portion of Extreme Numerics.NET. Also see the detailed data analysis math, and vector and matrix library feature lists.
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Descriptive Statistics
 Measures of central tendency: mean, median, trimmed mean, harmonic mean, geometric mean.
 Measures of scale: variance, standard deviation, range, interquartile range, absolute deviation from mean and median.
 Higher moments: skewness, kurtosis.
Probability Distributions
 Probability density function (PDF).
 Cumulative distribution function (CDF).
 Percentile or inverse cumulative distribution function.
 Moments: mean, variance, skewness and kurtosis.
 Generate random samples from any distribution.
 Parameter estimation for selected distributions Updated!
Continuous Probability Distributions
 Beta distribution.
 Cauchy distribution.
 Chisquared distribution.
 Erlang distribution.
 Exponential distribution.
 F distribution.
 Gamma distribution.
 Generalized Pareto distribution.
 Gumbel distribution.
 Inverse chisquare distribution.
 Inverse gamma distribution.
 Inverse Gaussian distribution.
 Inverse Weibull distribution.
 Laplace distribution.
 Logistic distribution.
 Loglogistic distribution.
 Lognormal distribution.
 Maxwell distribution.
 Normal distribution.
 Normal inverse Gaussian distribution.
 Pareto distribution.
 Piecewise distribution.
 Rayleigh distribution.
 Student t distribution.
 Transformed beta distribution.
 Transformed gamma distribution.
 Triangular distribution.
 General truncated distributions.
 Uniform distribution.
 Weibull distribution.
Discrete Probability Distributions
 Bernoulli distribution.
 Binomial distribution.
 Geometric distribution.
 Hypergeometric distribution.
 Logseries distribution.
 Negative binomial distribution.
 Poisson distribution.
 Uniform distribution.
Multivariate Probability Distributions
 Multivariate normal distribution.
 Dirichlet distribution.
 Wischart distribution.
Histograms
 Onedimensional histograms.
 Probability distribution associated with a histogram.
General Linear Models
 Infrastructure for General Linear Model and Generalized Linear Model calculations.
 Analysis of variance.
 Regression analysis.
 Modelspecific hypothesis tests.
Analysis of variance (ANOVA)
 One and twoway ANOVA.
 Posthoc tests for oneway ANOVA: Tukey, TukeyKramer, FisherHeyter, Scheffé
 Oneway ANOVA with repeated measures.
Regression analysis
 Simple, multiple, and polynomial regression.
 Ridge regression, LASSO, elastic net.
 Nonlinear regression.
 Logistic regression.
 Generalized linear models.
 Flexible regression models.
 Variancecovariance matrix, regression matrix.
 Confidence intervals and significance tests for regression parameters.
 Use Rstyle formulae to specify models.
Time series analysis
 ARIMA models.
 GARCH models.
 Treat several observation variables as a unit.
 Change frequency of time series.
 Automatically apply predefined aggregators.
 Advanced aggregators: volume weighted average.
Transformations of Time Series Data
 Lagged time series, sums, products.
 Change, percent change, growth rate.
 Extrapolated change, percent change, growth rate.
 Period to date sums and differences.
 Simple, exponential, weighted moving average.
 SavitskyGolay smoothing.
Multivariate Models
 Hierarchical clustering.
 Linkage: single, complete, average, centroid, Ward, median, McQuitty
 Continuous distance measures: Euclidean, squared Euclidean, maximum, Manhattan, Canberra, cosine, correlation, Minkowski
 Binary distance measures: binary matching, Jaccard, Russell, Hamann, dice, antidice, Sneath, Rogers, Ochiai, Yule, Anderberg, Kulczynski, Pearson
 Kmeans clustering.
 Initialize using: random centers, random assignments, Kmeans++
 Factor analysis.
 Factor methods: principal components, iterative principal axis, unweighted least squares, generalized least squares, maximum likelihood, alpha factoring, image factoring.
 Rotation methods: Varimax, Equamax, Quartimax, Parsimax, Promax.
 Scoring method: regression, Bartlett, AndersonRubin.

Principal Component Analysis (PCA).
 Partial Least Squares (PLS)
Statistical tests
 Tests for the mean: one sample ztest, one sample ttest.
 Paired and unpaired twosample t test for the difference between two sample means.
 Two Sample ztest for ratios.
 One sample chisquared test for variance.
 Ftest for the ratio of two variances.
 One and two sample KolmogorovSmirnov test.
 Tests for normality: AndersonDarling, ShapiroWilk
 Chisquared goodnessoffit test.
 Test for outliers: Grubbs’ test, Generalized ESD test.
 Bartlett and Levene tests for homogeneity of variances.
 McNemar and StuartMaxwell test.
Random number generation
 Compatible with the .NET Framework’s System.Random.
 Four generators, with varying quality, period and speed to suit your application.
 Generate random samples from any distribution.
 Quasirandom sequences: Fauré, Halton, Sobol sequences
 Shufflers and randomized enumerators