Distributions

The CSharpNumerics.Statistics.Distributions namespace provides probability distributions with a common IDistribution interface.

using CSharpNumerics.Statistics.Distributions;
using CSharpNumerics.Statistics.Random;

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📋 Available Distributions

Distribution	Class	Parameters
Uniform	UniformDistribution	$a, b$
Normal	NormalDistribution	$\mu, \sigma$
Exponential	ExponentialDistribution	$\lambda$
Poisson	PoissonDistribution	$\lambda$
Bernoulli	BernoulliDistribution	$p$
Binomial	BinomialDistribution	$n, p$
Student's t	StudentTDistribution	$\nu$ (degrees of freedom)
Chi-squared	ChiSquaredDistribution	$k$ (degrees of freedom)
F	FDistribution	$d_1, d_2$ (degrees of freedom)

Every distribution exposes Mean, Variance, StandardDeviation, Pdf(x), Cdf(x), Sample(rng) and Samples(rng, count).

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🔔 Normal Distribution

var normal = new NormalDistribution(mu: 100, sigma: 15);

double pdf = normal.Pdf(100);         // peak value
double cdf = normal.Cdf(115);         // P(X ≤ 115) ≈ 0.8413
double q   = normal.InverseCdf(0.95); // z such that P(X ≤ z) = 0.95

var rng = new RandomGenerator(42);
double[] samples = normal.Samples(rng, 10_000);

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🎯 Poisson Distribution

var poisson = new PoissonDistribution(lambda: 3.0);
double pmf   = poisson.Pdf(2);   // P(X = 2)
double cumul = poisson.Cdf(4);   // P(X ≤ 4)

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🪙 Binomial Distribution

var binomial = new BinomialDistribution(n: 10, p: 0.3);
// PMF sums to 1
double total = Enumerable.Range(0, 11).Sum(k => binomial.Pdf(k));

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📐 Student's t, Chi-squared & F Distributions

Used by the hypothesis testing methods, but can also be used directly:

var t = new StudentTDistribution(degreesOfFreedom: 29);
double pTwoTail = t.TwoTailedPValue(2.045);   // two-tailed p-value
double quantile  = t.InverseCdf(0.975);         // critical value

var chi2 = new ChiSquaredDistribution(degreesOfFreedom: 5);
double pUpper = chi2.UpperTailPValue(11.07);   // P(X ≥ 11.07)

var f = new FDistribution(d1: 3, d2: 20);
double pF = f.UpperTailPValue(3.10);           // P(F ≥ 3.10)