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Distributions

The tail probabilities and the quantile a caller holding its own statistic needs.

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.FisherSf(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 — these are the members a second package has asked for, and no more: four for Lodestar.Stats.Regression under decisions/0003, the chi-squared tail for a log-rank test under decisions/0003, and the normal quantile for that curve's confidence bounds under decisions/0003. The machinery underneath — log-gamma, the incomplete beta and gamma, the normal tail — stays internal; decisions/0003 says why, and the index page says what publishing them cost.

Applies to — net10.0, netstandard2.0.

See also — TTest, OneWayAnova, the distributions index.

Members

Member	What it does
Distributions.ChiSquaredSf	The upper tail of the chi-squared distribution.
Distributions.FisherSf	The upper tail of the F distribution.
Distributions.NormalQuantile	The value a standard normal falls below with a given probability.
Distributions.StudentQuantile	The value a Student's t falls below with a given probability.
Distributions.StudentSf	The upper tail of Student's t.