InverseCDF

The quantile function: the $x$ such that $CDF(dist, x) = q$.

InverseCDF(dist, q)numeric only — bisection against CDF, bracketed from Mean/Variance and widened geometrically otherwise. No exact closed forms are attempted (a documented divergence from Wolfram, which answers several of these symbolically); a non-numeric $q$ stays unevaluated.

Typed signatures

Type	Package	Applies
(distribution, real) -> real	statistics	always

Domain: Statistics

Details

• Generic over every distribution this package's CDF can evaluate numerically, old or new — including compute-engine's own natives.
• Median(dist) is the exact quantile at $1/2$ where one exists: a closed form for the common continuous laws, and for a discrete law with rational parameters the least $k$ whose CDF reaches $1/2$, decided in exact arithmetic. Other laws stay unevaluated; InverseCDF(dist, 1/2) gives the numeric value.

Plot

argument dist of type distribution has no control

Examples

Basic #

The median of a standard normal is 0 — bisection lands within double precision of it (deterministic, since the bisection is unseeded and non-random).

live ↗

In$\mathrm{InverseCDF}(\operatorname{NormalDistribution}(0, 1), \frac{1}{2})$Out$-6.957\,290\,979\,756\,837\cdot10^{-17}$

Unlike the numeric InverseCDF, a discrete median is exact: the least $k$ whose CDF reaches $1/2$, decided in exact arithmetic

live ↗

In$\mathrm{median}(\operatorname{PoissonDistribution}(12))$Out$12$

Scope #

live ↗

In$\mathrm{median}(\operatorname{BinomialDistribution}(25, \frac{1}{7}))$Out$3$

About

Examples	3
Checked against	Wolfram Language 2 agree

See also: CDF, SurvivalFunction, Median