# 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.

### 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