Probability Distributions
In MathNet.Numerics.Distributions we provide a wide range of probability distributions. Once parametrized, they can be used to sample non-uniform random numbers or investigate their statistical properties.All the distributions implement a basic set of operations such as computing the mean, standard deviation, density, etc. Because it is often numerically more stable and faster to compute quantities in the log domain, we also provide a selection of them, including Density, in the logarithmic domain with the "Ln" suffix, .e.g. DensityLn.
using MathNet.Numerics.Random; using MathNet.Numerics.Distributions; var gamma = new Gamma(2.0, 1.5); var mean = gamma.Mean; var variance = gamma.Variance; var entropy = gamma.Entropy; // ...var a = gamma.Density(2.3); // pdfvar b = gamma.DensityLn(2.3); // ln(pdf)var c = gamma.CumulativeDistribution(0.7); // cdf
Parametrizing the Distributions
There are many ways to parameterize a distribution in the literature. When using the default constructor, study carefully which parameters it requires. If they do not suite your needs, there will likely be static method which can construct the distribution for you with the parameters of your choice. For example, to construct a normal distribution with mean 0.0 and standard deviation 2.0 you can use var n = new Normal(0.0, 2.0); . However, if you'd rather parameterize the normal distribution using a mean and precision, one can use the following code instead: var n = Normal.WithMeanPrecision(0.0,0.5);var gamma = Gamma.WithShapeScale(2.0, 0.75);Random Number Sampling
Each distribution provides methods to generate random numbers from that distribution. These random variate generators work by accessing the distribution's member RandomSource (which is a subclass of System.Random, see Random Numbers for details) to provide uniform random numbers. By default, this member is an instance of System.Random but one can easily replace this with more sophisticated random number generators from MathNet.Numerics.Random. Each distribution class has two static and two class methods: for each pair (static and class), one of them generates a single sample, the other will generate an IEnumerable<T> of samples. The static methods allow random number generation without instantiating the actual class.var gamma = new Gamma(2.0, 1.5); gamma.RandomSource = new MersenneTwister(); double a = gamma.Sample(); double[] b = gamma.Samples().Take(100).ToArray();
var rnd = new MersenneTwister(); double a = Gamma.Sample(rnd, 2.0, 1.5); double[] b = Gamma.Samples(rnd, 2.0, 1.5).Take(10).ToArray();
Probability Distributions in F#
The F# extensions provide a few simple helper functions in the MathNet.Numerics.Distributions namespace to assign a specific random source to a distribution: withRandom, withSystemRandom, withCryptoRandom and withMersenneTwister:let rnd = Random.xorshift () let normal = Normal.WithMeanVariance(3.0, 1.5) |> withRandom rnd let gamma = new Gamma(2.0, 1.5) |> withMersenneTwister let cauchy = new Cauchy() |> withRandom (Random.mrg32k3aWith 10 false) let samples = cauchy.Samples() |> Seq.take 100 |> List.ofSeq let samples2 = Cauchy.Samples(rnd, 1.0, 3.0) |> Seq.take 20 |> List.ofSeq
Discrete Distributions
All discrete distributions implement the IDiscreteDistribution and IDistribution intefaces.- Discrete Uniform
- Bernoulli
- Binomial
- Negative Binomial
- Geometric
- Hybergeometric
- Poisson
- Categorical
- Conway-Maxwell-Poisson
- Zipf
Continuous Distributions
All continuous distributions implement the IContinuousDistribution and IDistribution intefaces.- Continuous Uniform
- Normal
- Log Normal
- Beta
- Cauchy (Cauchy-Lorentz)
- Chi
- Chi Square
- Erlang
- Exponential
- Fisher-Snedecor (F-Distribution)
- Gamma
- Inverse Gamma
- Laplace
- Pareto
- Rayleigh
- Stable
- Stundets-T
- Weibull
Triangular
