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Distributions.FisherSnedecorPdf

The F density.

public static double FisherSnedecorPdf(double f, double numeratorDf, double denominatorDf)

Parameters — f is the point; below zero the density is zero, NaN answers NaN, and +∞ answers zero up to a numerator of two and NaN past it, as scipy's does. numeratorDf and denominatorDf are the two degrees of freedom, each of which must be positive and finite.

Returns — scipy.stats.f.pdf(f, dfn, dfd).

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

Example — the density at one, for a model with two regressors and twenty residual degrees of freedom.

using Lodestar.Stats;

double atOne = Distributions.FisherSnedecorPdf(1.0, 2.0, 20.0);   // => 0.350493…

Remarks — At zero the density follows the first shape as scipy's does: infinite when numeratorDf < 2, finite at 2, zero above. Where numeratorDf · f overflows it is zero.

Past shapes of a million this is more exact than scipy's. The density reduces to y^a (1 − y)^b / (B(a, b) f) with y = d₁f/(d₁f + d₂), both y and 1 − y formed by division rather than one as one minus the other, and B from Stirling's series. scipy's own density is 5e-7 off at (1e8, 1e8) and 1e-5 at (1e10, 1) against a 60-digit reference, which this one holds to 1e-12.

Applies to — net10.0, netstandard2.0.

See also — Distributions.FisherSnedecorCdf, Distributions.FisherSnedecorSf.