Distributions are assignments of a probability-weight to each of the elements in a set. Most commonly, those sets are subsets of the integers or real numbers.
Distribution on the integers inherit from the abstract DiscreteDistribution class. For any discrete distribution, you can determine its range (called Support), the probability weight of each value (using ProbabilityMass(Int32)), and many other properties. You can generate pseduo-random integers distributed according to a discrete distribution (using GetRandomValue(Random)). Many discrete distributions are defined, including PoissonDistribution and BinomialDistribution.
Distributions on the real numbers inherit from the abstract ContinuousDistribution class. For any continuous distribution, you can determine its range (called Support), the probability density at each value (using ProbabilityDensity(Double)), the cumulative distribution function (using LeftProbability(Double)), and many other properties. You can generate pseudo-random floating-point values distributed according to a continuous distribution (using GetRandomValue(Random)). Many continuous distributions are defined, including NormalDistribution, BetaDistribution, GammaDistribution, and WeibullDistribution.
All one-dimensional distibutions, continuous and discrete, inherit from the abstract UnivariateDistribution class. Using the properties and methods of this class, you can determine raw moments (RawMoment(Int32)) such as the Mean, central moments (CentralMoment(Int32)) such as the Variance, or cumulants (Cumulant(Int32)).
Many distributions also offer methods that allow you to find the parameters that best fit a given set of data points and measure the quality of the fit.
You can add your own continous and discrete distributions by inheriting from ContinuousDistribution or DiscreteDistribution and implementing only a few abstract methods. All the remaining properties and methods are then automatically determined for your distribution.
| BenfordDistribution | Represents a Benford distribution. |
| BernoulliDistribution | Represents a Bernoulli distribution. |
| BernoulliFitResult | Represents the result of a fit to a Bernoulli distribution. |
| BetaDistribution | Represents a beta distribution. |
| BetaFitResult | Contains the result of a fit of a sample to a Beta distribution. |
| BinomialDistribution | Represents a discrete binomial distribution. |
| CauchyDistribution | Represents a Cauchy distribution. |
| ChiDistribution | Represents a χ distribution. |
| ChiSquaredDistribution | Represents a χ2 distribution. |
| ContinuousDistribution | Represents all continuous, univariate probability distributions. |
| DiscreteDistribution | Represents all discrete, univariate probability distributions. |
| DiscreteUniformDistribution | Describes a discrete uniform distribution. |
| DistributionFitResultT | Represents the result of a fit to a distribution. |
| ExponentialDistribution | Represents an exponential distribution. |
| ExponentialFitResult | Represents the result of a fit to the exponential distribution. |
| FisherDistribution | Represents the distribution of Fisher's F-statistic. |
| FrechetDistribution | Represents a Fréchet distribution. |
| GammaDistribution | Represents a Gamma distribution. |
| GammaFitResult | Contains the result of a fit of a sample to a gamma distribution. |
| GeometricDistribution | Represents a geometric distribution. |
| GumbelDistribution | Represents a Gumbel distribution. |
| GumbelFitResult | Represents the result of fitting sample data to a Gumbel distribution. |
| HypergeometricDistribution | Represents a hypergeometric distribution. |
| KolmogorovDistribution | Represents the distribution of the Kolmogorov-Smirnov D statistic. |
| KuiperDistribution | Represents the asymptotic distribution of Kuiper's V statistic. |
| LaplaceDistribution | Represents a Laplace distribution. |
| LogisticDistribution | Represents a logistic distribution. |
| LognormalDistribution | Represents a log-normal distribution. |
| LognormalFitResult | Contains the result of a fit to a log-normal distribution. |
| MomentMath | Contains methods for converting between different kinds of moments. |
| NegativeBinomialDistribution | Represents a negative binomial distribution. |
| NoncentralChiSquaredDistribution | Represents a non-central chi squared distribution. |
| NormalDistribution | Represents a normal (Gaussian) distribution. |
| NormalFitResult | Represents the result of a sample to a normal distribution. |
| ParetoDistribution | Represents a Pareto or power law distribution. |
| PearsonRDistribution | Represents the distribution of Pearsons's r statistic. |
| PoissonDistribution | Represented a Poisson distribution. |
| RayleighDistribution | Represents a Rayleigh distribution. |
| RayleighFitResult | Contains the result of a fit to a Rayleigh distribution. |
| SkellamDistribution | Represents a Skellam distribution. |
| SkewNormalDistribution | Represents a standard skew nomral distribution. |
| StudentDistribution | Represents the distribution of Student's t statistic. |
| TriangularDistribution | Represents a triangular distribution. |
| UniformDistribution | Represents a uniform distribution over an interval. |
| UnivariateDistribution | Represents a probability distribution over a single variable. |
| WaldDistribution | Represents a Wald (Inverse Gaussian) distribution. |
| WaldFitResult | Contains the result of the fit of a sample to a Wald (Inverse Gaussian) distribution. |
| WeibullDistribution | Represents a Weibull distribution. |
| WeibullFitResult | Represents the result of a sample to a normal distribution. |