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Distributions.ChiSquaredPdf

The chi-squared density.

public static double ChiSquaredPdf(double x, double df)

Parameters — x is the point; below zero the density is zero, NaN answers NaN, and +∞ answers zero, the density's limit at every df, where scipy's formula forms ∞/∞ past two and answers NaN (decision 0010). df is the degrees of freedom, which must be positive and finite.

Returns — scipy.stats.chi2.pdf(x, df).

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

Example — the density at two, on four degrees of freedom.

using Lodestar.Stats;

double atTwo = Distributions.ChiSquaredPdf(2.0, 4.0);   // => 0.183939…

Remarks — The incomplete gamma's prefactor (x/2)^(k/2) e^(−x/2) / Γ(k/2) over x, which past ten degrees of freedom forms no term of order k log k. At zero the density follows df as scipy's does: infinite below two, one half at two, zero above.

Applies to — net10.0, netstandard2.0.

See also — Distributions.ChiSquaredCdf, Distributions.ChiSquaredSf.