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Distributions

The density, both tails and both inverses of the standard normal, Student's t, F and chi-squared laws, as scipy.stats gives them.

public static class Distributions

Example — a coefficient's two-sided p-value and its 95% multiplier, the two numbers a regression table prints beside an estimate.

using Lodestar.Stats;

// A t of 2.0 on 12 residual degrees of freedom.
double twoSided = 2.0 * Distributions.StudentSf(2.0, 12.0);   // => 0.0686550…
double multiplier = Distributions.StudentQuantile(0.975, 12.0); // => 2.1788128296672298

// And the overall F test of a model with two regressors and twenty residual df.
double overall = Distributions.FisherSnedecorSf(4.0, 2.0, 20.0);        // => 0.0345716…

// And a log-rank test's p-value, on one degree of freedom.
double logRank = Distributions.ChiSquaredSf(3.84, 1.0);          // => 0.0500…

// The large-sample multiplier, where a Student one has no degrees of freedom to take.
double large = Distributions.NormalQuantile(0.975);              // => 1.959963…

Remarks — twenty members, Pdf, Cdf, Sf, Quantile (scipy's ppf) and Isf for each law. Five were published first because a sibling package asked for them, under decisions/0003; the other fifteen followed in #1158, so a caller writing their own test, interval or power calculation no longer leaves the package for the law underneath it. Each tail is evaluated on the side that keeps full relative precision, and the log-gamma, incomplete beta and gamma and their inverses stay internal. The index page has the history.

Applies to — net10.0, netstandard2.0.

See also — TTest, OneWayAnova, the distributions index.

Members

Member	What it does
Distributions.ChiSquaredCdf	The lower tail of the chi-squared distribution.
Distributions.ChiSquaredIsf	The inverse of the chi-squared upper tail.
Distributions.ChiSquaredPdf	The chi-squared density.
Distributions.ChiSquaredQuantile	The value a chi-squared falls below with a given probability.
Distributions.ChiSquaredSf	The upper tail of the chi-squared distribution.
Distributions.FisherSnedecorCdf	The lower tail of the F distribution.
Distributions.FisherSnedecorIsf	The inverse of the F upper tail.
Distributions.FisherSnedecorPdf	The F density.
Distributions.FisherSnedecorQuantile	The value an F falls below with a given probability.
Distributions.FisherSnedecorSf	The upper tail of the F distribution.
Distributions.FisherSf	Its former name, obsolete, kept for binaries compiled against 0.5.0.
Distributions.NormalCdf	The lower tail of the standard normal.
Distributions.NormalIsf	The inverse of the standard normal's upper tail.
Distributions.NormalPdf	The standard normal density.
Distributions.NormalQuantile	The value a standard normal falls below with a given probability.
Distributions.NormalSf	The upper tail of the standard normal.
Distributions.StudentCdf	The lower tail of Student's t.
Distributions.StudentIsf	The inverse of Student's t upper tail.
Distributions.StudentPdf	Student's t density.
Distributions.StudentQuantile	The value a Student's t falls below with a given probability.
Distributions.StudentSf	The upper tail of Student's t.