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Distributions.ChiSquaredSf

The upper tail of the chi-squared distribution: P(X > x).

public static double ChiSquaredSf(double x, double df)

Parameters — x is the statistic. df is the degrees of freedom, which must be positive and finite.

Returns — scipy.stats.chi2.sf(x, df).

Exceptions — ArgumentOutOfRangeException when df is not positive, NaN included. x is not refused: the distribution has no mass below zero, so a non-positive statistic returns one rather than throwing. A df of 5e-324, whose half is not a double, is refused too (#1690).

Example — a log-rank test on two groups carries one degree of freedom.

using Lodestar.Stats;

double logRank = Distributions.ChiSquaredSf(3.84, 1.0);  // => 0.0500…

// Four degrees of freedom, as a k-sample comparison of five groups would have.
double kSample = Distributions.ChiSquaredSf(9.488, 4.0);  // => 0.0499…

// Far into the tail, where an absolute tolerance would accept a zero.
double extreme = Distributions.ChiSquaredSf(120.0, 3.0);  // => 7.716…

Remarks — the same tail ChiSquared.GoodnessOfFit and ChiSquared.Contingency already report, exposed for a caller that computed its own statistic rather than handing this package a table. A log-rank test is the case that asked for it.

Below the support it answers one, and does not throw. The regularized incomplete gamma underneath validates its own argument, so a negative statistic would otherwise surface an internal helper's parameter name out of a public method. Returning one is also the right answer: the whole mass lies above.

Routing a statistic through here and through the chi-squared tests above gives the same p-value to the last bit, because it is the same function and not a second approximation — which is the agreement decision 0003 argued a re-derived tail would lose.

Applies to — net10.0, netstandard2.0.

See also — ChiSquared.Contingency, Distributions.FisherSnedecorSf.