# Probability And Statistics For .net

This suite consists of six packages: Statistics, Discrete Probability, Standard Probability Distributions, Curve Fitting, Hypothesis Testing, and Correlation & Regression which offer the following functionality.

Statistics Module
The Statistics module incorporates topic from data presentation (incl. standard, relative and cumulative frequency tables), Basic Statistics (incl. measure of centrality, dispersion and relative location), Grouped Data (incl. Sample Mean, Variance and Standard Deviation) and Quality Control(incl. R-Chart, S-Chart and Median Chart).

Discrete Probability Module
The Discrete Probability module encapsulates the probabilistic study of finite set of events (i.e. discrete probability) and experiments with a finite number of outcomes (i.e. discrete random variables). Including: probability measures, union/intersection law, conditionals/complementary probability; cumulative distribution functions, mean/variance/expected return of Random Variable.

Standard Probability Distributions Module
This module assists in the development of applications that incorporate the Binomial, Poisson, Normal, Lognormal, Pareto, Uniform, Hypergeometric, Weibull and Exponential probability distributions. The probability density function, cumulative distribution function and inverse, mean, variance, Skewness and Kurtosis are implemented where appropriate and/or their approximations for each distribution. We also offer methods which randomly generate numbers from a given distribution.

Curve Fitting
Allows the fitting of linear and non-linear functions for a data set which may or may not exhibit measurement errors in accordance with the least squares approach. A general linear algorithm and the specialized Levenberg-Marquardt algorithm to handle the non-linear case are provided. We also include functionality which performs ANNOVA type analysis including goodness-of-fit measures such as the R-Squared measure and T-Test statistic.

Confidence Intervals and Hypothesis Testing Module
Within this component we present two aspects of inferential statistics known as confidence intervals and hypothesis testing. Confidence intervals determine the level of confidence in pointwise statistics (e.g. mean, variance) of the sample in relation to the statistics for the entire population. With hypothesis testing the user can judge which of several hypotheses sampled evidence best supports.

Correlation and Regression Module
Allows the user to investigate relationships between two variables. These finding can be used to predict one variable from the given values of other variables. We cover linear (Spearman's, t-test, z-transform) and rank (Spearman's, Kendall's) correlation, linear regression and conditional means.

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