# 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.

### 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