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Distributions.ChiSquaredQuantile

The value a chi-squared falls below with probability p.

public static double ChiSquaredQuantile(double p, double df)

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

Returns — scipy.stats.chi2.ppf(p, df).

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

Example — the 95% point on one degree of freedom, and the lower bound of a variance interval.

using Lodestar.Stats;

double critical = Distributions.ChiSquaredQuantile(0.95, 1.0);   // => 3.841458…
double lower = Distributions.ChiSquaredQuantile(0.025, 10.0);    // => 3.246972…

Remarks — The incomplete gamma inverted by Newton on its logarithm against log x, in a bracket that grows until an evaluation closes it, seeded by Wilson-Hilferty or, deep in the lower tail, by the leading term x^a / Γ(a + 1). Whichever of p and 1 − p is smaller is the one solved.

Applies to — net10.0, netstandard2.0.

See also — Distributions.ChiSquaredIsf, Distributions.ChiSquaredCdf.