The OpenD Programming Language

binomialCDF

mir stat distribution binomial

Computes the binomial cumulative distribution function (CDF).

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

  1. T binomialCDF(size_t k, size_t n, T p)
    template binomialCDF(BinomialAlgo binomialAlgo = BinomialAlgo.direct, PoissonAlgo poissonAlgo = PoissonAlgo.gamma)
    @safe pure nothrow @nogc
    T
    binomialCDF
    (
    T
    )
    (
    const size_t k
    ,
    const size_t n
    ,
    const T p
    )
    if (
    isFloatingPoint!T
    )
  2. template binomialCDF(string binomialAlgo, string poissonAlgo = "gamma")

Members

Functions

binomialCDF
T binomialCDF(size_t k, size_t n, T p)

Parameters

binomialAlgo

algorithm for calculating CDF (default: BinomialAlgo.direct)

poissonAlgo

algorithm for poisson approximation (default: PoissonAlgo.gamma)

Examples

import mir.math.common: approxEqual, pow;

assert(4.binomialCDF(6, 2.0 / 3).approxEqual(binomialPMF(0, 6, 2.0 / 3) + binomialPMF(1, 6, 2.0 / 3) + binomialPMF(2, 6, 2.0 / 3) + binomialPMF(3, 6, 2.0 / 3) + binomialPMF(4, 6, 2.0 / 3)));
// For large values of `n` with `p` not too extreme, can approximate with normal distribution
assert(550_000.binomialCDF!"approxNormal"(1_000_000, 0.55).approxEqual(0.5));
// Or closer with continuity correction
assert(550_000.binomialCDF!"approxNormalContinuityCorrection"(1_000_000, 0.55).approxEqual(0.500401));
// Poisson approximation is better when `p` is low
assert(10_000.binomialCDF!"approxPoisson"(1_000_000, 0.01).approxEqual(0.5026596));

See Also

Binomial Distribution

Meta

Source

See Implementation

mir stat distribution binomial enumsfunctionstemplates
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