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Distributions.FisherSnedecorQuantile

The value an F falls below with probability p.

public static double FisherSnedecorQuantile(double p, double numeratorDf, double denominatorDf)

Parameters — p is a probability in [0, 1]; 0 answers 0 and 1 answers +∞. numeratorDf and denominatorDf are the two degrees of freedom, each of which must be positive and finite.

Returns — scipy.stats.f.ppf(p, dfn, dfd).

Exceptions — ArgumentOutOfRangeException when p is outside [0, 1], NaN included, or when either degrees of freedom is not positive. A df of 5e-324, whose half is not a double, is refused too (#1690).

Example — the 5% critical value of an overall test on two and twenty degrees of freedom.

using Lodestar.Stats;

double critical = Distributions.FisherSnedecorQuantile(0.95, 2.0, 20.0);   // => 3.492828…

Remarks — Inverts the incomplete beta for both y and 1 − y, refining by Newton on whichever of the two is below one half, so neither is one minus a number near one: at shapes (1e10, 1) the root sits 2e-10 below one, and forming 1 − y from it was 1e-7 off. Where scipy disagrees, scipy is checked against itself: at p = 1e-100 with dfn = 0.5 it answers 1.3e-307, whose own lower tail is 1.4e-77; the true point underflows, and this answers zero. docs/equivalence.md lists these points.

Applies to — net10.0, netstandard2.0.

See also — Distributions.FisherSnedecorIsf, Distributions.FisherSnedecorCdf.