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Latest version 8.1.20 (August 2023)

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Extreme Optimization Numerical Libraries for .NET

Statistics Library Features

Below is a list of features for the statistics library portion of the Extreme Optimization Numerical Libraries for .NET. Also see the detailed data analysis mathematics, 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.
  • Chi-squared distribution.
  • Erlang distribution.
  • Exponential distribution.
  • F distribution.
  • Gamma distribution.
  • Generalized Pareto distribution.
  • Gumbel distribution.
  • Inverse chi-square distribution.
  • Inverse gamma distribution.
  • Inverse Gaussian distribution.
  • Inverse Weibull distribution.
  • Laplace distribution.
  • Logistic distribution.
  • Log-logistic 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.
  • Log-series distribution.
  • Negative binomial distribution.
  • Poisson distribution.
  • Uniform distribution.

Multivariate Probability Distributions

  • Multivariate normal distribution.
  • Dirichlet distribution.
  • Wischart distribution.


  • One-dimensional 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.
  • Model-specific hypothesis tests.

Analysis of variance (ANOVA)

  • One and two-way ANOVA.
  • Post-hoc tests for one-way ANOVA: Tukey, Tukey-Kramer, Fisher-Heyter, Scheffé
  • One-way ANOVA with repeated measures.

Regression analysis

  • Simple, multiple, and polynomial regression
  • Nonlinear regression
  • Logistic regression
  • Generalized linear models
  • Flexible regression models.
  • Variance-covariance matrix, regression matrix.
  • Confidence intervals and significance tests for regression parameters.

Time series analysis

  • 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.
  • Savitsky-Golay 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, anti-dice, Sneath, Rogers, Ochiai, Yule, Anderberg, Kulczynski, Pearson
  • K-means clustering.
    • Initialize using: random centers, random assignments, K-means++
  • 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, Anderson-Rubin.
  • Principal Component Analysis (PCA).

Statistical tests

  • Tests for the mean: one sample z-test, one sample t-test.
  • Paired and unpaired two-sample t test for the difference between two sample means.
  • Two Sample z-test for ratios.
  • One sample chi-squared test for variance.
  • F-test for the ratio of two variances.
  • One and two sample Kolmogorov-Smirnov test.
  • Tests for normality: Anderson-Darling, Shapiro-Wilk
  • Chi-squared goodness-of-fit test.
  • Test for outliers: Grubbs' test, Generalized ESD test.
  • Bartlett and Levene tests for homogeneity of variances.
  • McNemar and Stuart-Maxwell 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.
  • Quasi-random sequences: Fauré, Halton, Sobol sequences
  • Shufflers and randomized enumerators