Lodestar.Stats 0.4.0. This page is frozen at that release. Read the current documentation for what main says now. A link to a decision or a migration page follows main, and leaves the archive.

Distribution tails — Lodestar.Stats

One type, Distributions: the tail probabilities and the quantile a caller holding its own statistic needs, without going through a hypothesis test to reach them.

Why only four members

This package computes every tail it needs from its own log-gamma, incomplete beta and incomplete gamma, and decisions/0081 kept that layer internal — deliberately, and with the condition for changing its mind written down: "publishing later stays possible the day a second package needs the same functions."

Lodestar.Stats.Regression is that day. What it needs is a Student tail for each coefficient's p-value, a Student quantile for each confidence interval, and an F tail for the overall test. Those three are published. The log-gamma, the incomplete beta and gamma, the normal tail and the finite-sample Kolmogorov distribution underneath them stay internal, because nothing has asked for them and an unpublished API can still be published later — the reverse is not true.

What publishing cost

A parity promise of its own. The internal tests check these functions against closed forms, which is enough for a p-value near 0.05 and says nothing about the far tail. The corpus behind this page replays scipy.stats down to 3.1e-24, compared relatively: an absolute 1e-9 there would accept an implementation returning zero.

It also cost a correction. The internal helper behind Distributions.StudentQuantile solves P(T > x) = p and therefore carries the opposite sign to a quantile. Published under its own name unchanged, it would have handed a caller -2.18 where every table prints +2.18.

Types

Type	What it is
Distributions	Two Student tails and the F tail, for a caller holding its own statistic.

See also

• Hypothesis tests — the ten families built on the same machinery.
• Python → C# equivalence.