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Distributions.StudentCdf

Student's t lower tail: P(T ≤ t).

public static double StudentCdf(double t, double df)

Parameters — t is the statistic; NaN answers NaN. df is the degrees of freedom, which must be positive; +∞ is the standard normal law, as scipy's is.

Returns — scipy.stats.t.cdf(t, df), the upper tail of −t; from df 1e20 the normal law's lower tail, and to df 1e-12 the first-order ½ + (df/2) asinh(t/√df), one half at every finite t to df 1e-20, where scipy's reads 1 at t = 1e300 (#1690).

Exceptions — ArgumentOutOfRangeException when df is not positive, NaN included.

Example — a one-sided lower p-value on ten degrees of freedom.

using Lodestar.Stats;

double lower = Distributions.StudentCdf(-2.0, 10.0);   // => 0.036694…

Remarks — The upper tail of −t, by the law's symmetry, so a small lower tail keeps its digits.

Applies to — net10.0, netstandard2.0.

See also — Distributions.StudentSf, Distributions.StudentQuantile.