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Distributions.StudentQuantile

The value a Student's t falls below with probability p.

public static double StudentQuantile(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.ppf(p, df).

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

Example — the multiplier a 95% interval asks for.

using Lodestar.Stats;

double multiplier = Distributions.StudentQuantile(0.975, 12.0);  // => 2.1788128296672298

// It is the value whose upper tail is the other 2.5%.
double tail = Distributions.StudentSf(multiplier, 12.0);          // => 0.024999999999999998

// An interval is then estimate ± multiplier × standard error.
double halfWidth = multiplier * 0.4;                              // => 0.871525…

Remarks — this is the quantile, not the inverse survival function, and the distinction is not pedantic. The internal helper it delegates to solves P(T > x) = p and therefore carries the opposite sign; the two are related by the distribution's symmetry about zero. Published under that helper's own convention, this method would have returned -2.18 where every printed table shows +2.18, and an interval built on it would have been reflected through its own estimate.

The endpoints answer the two infinities, as scipy's do. They were refused until #1158, which aligned every quantile of this class on the reference's support ends.

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.StudentSf, Distributions.FisherSnedecorSf.