The OpenD Programming Language

hypergeometricPMF

Computes the hypergeometric probability mass function (PMF).

Additional algorithms may be provided for calculating PMF that allow trading off time and accuracy. If approxPoisson is provided, PoissonAlgo.gamma is assumed.

Examples

import mir.test: shouldApprox;

0.hypergeometricPMF(7, 4, 3).shouldApprox == 0.02857143;
1.hypergeometricPMF(7, 4, 3).shouldApprox == 0.3428571;
2.hypergeometricPMF(7, 4, 3).shouldApprox == 0.5142857;
3.hypergeometricPMF(7, 4, 3).shouldApprox == 0.1142857;

// can also provide a template argument to change output type
static assert(is(typeof(hypergeometricPMF!float(3, 7, 4, 3)) == float));

Alternate algorithms

import mir.test: shouldApprox;
import mir.math.common: exp;

// Can approximate hypergeometric with binomial distribution
20.hypergeometricPMF!"approxBinomial"(750_000, 250_000, 50).shouldApprox == exp(hypergeometricLPMF(20, 750_000, 250_000, 50));
// Can approximate hypergeometric with poisson distribution
20.hypergeometricPMF!"approxPoisson"(100_000, 100, 5_000).shouldApprox == exp(hypergeometricLPMF(20, 100_000, 100, 5_000));
// Can approximate hypergeometric with normal distribution
3_500.hypergeometricPMF!"approxNormal"(10_000, 7_500, 5_000).shouldApprox == exp(hypergeometricLPMF(3_500, 10_000, 7_500, 5_000));
// Can approximate hypergeometric with normal distribution (with continuity correction)
3_500.hypergeometricPMF!"approxNormalContinuityCorrection"(10_000, 7_500, 5_000).shouldApprox == exp(hypergeometricLPMF(3_500, 10_000, 7_500, 5_000));

See Also

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