hypergeometricInvCDF

Computes the hypergeometric inverse cumulative distribution function (InvCDF).

Additional algorithms may be provided for calculating InvCDF that allow trading off time and accuracy. If approxPoisson is provided, PoissonAlgo.direct is assumed. This is different from other functions that use PoissonAlgo.gamma since in this case it does not provide the same result.

Setting hypergeometricAlgo = HypergeometricAlgo.direct results in direct summation being used, which can result in significant slowdowns for large values of k.

size_t hypergeometricInvCDF(T p, size_t N, size_t K, size_t n)
@safe pure @nogc nothrow
size_t
hypergeometricInvCDF
(
T
HypergeometricAlgo hypergeometricAlgo = HypergeometricAlgo.direct
)
(
const T p
,
const size_t N
,
const size_t K
,
const size_t n
)
if (
isFloatingPoint!T
)
template hypergeometricInvCDF(T, string hypergeometricAlgo)
template hypergeometricInvCDF(string hypergeometricAlgo)

Parameters

p T: value to evaluate InvCDF
N size_t: total population size
K size_t: number of relevant objects in population
n size_t: number of draws

Examples

import mir.test: should;

0.0.hypergeometricInvCDF(40, 15, 20).should == 0;
0.1.hypergeometricInvCDF(40, 15, 20).should == 6;
0.2.hypergeometricInvCDF(40, 15, 20).should == 6;
0.3.hypergeometricInvCDF(40, 15, 20).should == 7;
0.4.hypergeometricInvCDF(40, 15, 20).should == 7;
0.5.hypergeometricInvCDF(40, 15, 20).should == 7;
0.6.hypergeometricInvCDF(40, 15, 20).should == 8;
0.7.hypergeometricInvCDF(40, 15, 20).should == 8;
0.8.hypergeometricInvCDF(40, 15, 20).should == 9;
0.9.hypergeometricInvCDF(40, 15, 20).should == 9;
1.0.hypergeometricInvCDF(40, 15, 20).should == 15;

Alternate algorithms

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

// Can approximate hypergeometric with binomial distribution
0.5.hypergeometricInvCDF!"approxBinomial"(750_000, 250_000, 50).shouldApprox!double == 17;
// Can approximate hypergeometric with poisson distribution
0.4.hypergeometricInvCDF!"approxPoisson"(100_000, 100, 5_000).shouldApprox!double == 4;
// Can approximate hypergeometric with normal distribution
0.6.hypergeometricInvCDF!"approxNormal"(10_000, 7_500, 5_000).shouldApprox!double == 3755;
// Can approximate hypergeometric with normal distribution
0.6.hypergeometricInvCDF!"approxNormalContinuityCorrection"(10_000, 7_500, 5_000).shouldApprox!double(1) == 3755;

The OpenD Programming Language

hypergeometricInvCDF

Parameters

Examples

See Also

Meta

Source