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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.
Download the trial version today!
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.
Histograms
- 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
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