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Distributions.StudentIsf

The t with P(T > t) = p: the inverse of StudentSf.

public static double StudentIsf(double p, double df)

Parameters — p is a probability in [0, 1]; 0 answers +∞ and 1 answers −∞. df is the degrees of freedom, which must be positive; +∞ is the standard normal law, as scipy's is.

Returns — scipy.stats.t.isf(p, df), except where the root lies past the largest double, at a df below 1.05 and p near one half or tiny: ±∞ there, where scipy answers finite values that are roots of no tail (t.isf(0.4, 1e-300) is 6703.9), and every p but one half from df 1e-20 down (#1690).

Exceptions — ArgumentOutOfRangeException when p is outside [0, 1], NaN included, or when df is not positive.

Example — the upper 2.5% point on twelve degrees of freedom.

using Lodestar.Stats;

double upper = Distributions.StudentIsf(0.025, 12.0);   // => 2.178812…

Remarks — The mirror of StudentQuantile. It reaches past 1.3e154: the Cauchy's (df = 1) point at 1e-300 is 1/(π·1e-300) = 3.18e299, which an overflowing t² used to cap (#1158).

A point past the largest double, such as the 1e-300 point on half a degree of freedom near 1e600, is ±∞ rather than ±1.8e308.

Applies to — net10.0, netstandard2.0.

See also — Distributions.StudentQuantile, Distributions.StudentSf.