Extreme Optimization > Statistics Features

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Extreme Optimization Numerical Libraries for .NET

Statistics Features

General features of the Extreme Optimization Statistics Library for .NET:

• Easy to use even for the mathematically not-so-inclined
• Powerful enough to satisfy the most demanding power user.
• Intuitive object model. The objects in Extreme Optimization Statistics Library for .NET and the relationships between them match our every-day concepts.
• Great performance through optimized implementation of the best algorithms.
• Cross-platform. Works out-of-the-box on 32 and 64 bit platforms, .NET versions 1.1, 2.0, 3.0, 3.5.

Below is a list of features for the statistics library portion of the Extreme Optimization Numerical Libraries for .NET. Also see the detailed Mathematics Library 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 New!

Continuous Probability Distributions

• Beta distribution.
• Cauchy distribution.
• Chi-squared distribution.
• Erlang distribution.
• Exponential distribution.
• F distribution.
• Gamma distribution.
• Generalized Pareto distribution. New!
• Gumbel distribution.
• Laplace distribution.
• Logistic distribution.
• Lognormal distribution.
• Normal distribution.
• Pareto distribution.
• Piecewise distribution. New!
• Rayleigh distribution.
• Student t distribution.
• Transformed beta distribution. New!
• Transformed gamma distribution. New!
• Triangular distribution.
• Uniform distribution.
• Weibull distribution.

Discrete Probability Distributions

• Bernoulli distribution.
• Binomial distribution.
• Geometric distribution.
• Hypergeometric distribution.
• Negative binomial distribution.
• Poisson distribution.
• Uniform distribution.

Histograms

• One-dimensional histograms.
• Probability distribution associated with a histogram.

General Linear Model

• 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.
• One-way ANOVA with repeated measures.

Regression analysis

• Simple, multiple, and polynomial regression
• Nonlinear regression
• Logistic regression New!
• Flexible regression models.
• Variance-covariance matrix, regression matrix.
• Confidence intervals for regression parameters.

Time series analysis

• Treat several observation variables as a unit New!
• Change frequency of time series New!
• Automatically apply predefined aggregators New!
• Advanced aggregators: volume weighted average New!

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

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 New!
• One sample chi-squared test for variance.
• F-test for the ratio of two variances.
• One and two sample Kolmogorov-Smirnov test.
• Anderson-Darling test for normality.
• Chi-squared goodness-of-fit test.
• Bartlett and Levene tests for homogeneity of variances.
• McNemar and Stuart-Maxwell test. New!

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.
• Faur and Halton sequences
• Shufflers and randomized enumerators

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