regularizedIncompleteBeta
regularizedIncompleteBeta(
a,b,x,options?):number
Defined in: packages/math-analysis/src/regularized-incomplete-beta.ts:47
The regularized incomplete beta Iₓ(a, b) — the fraction of a Beta(a, b)
distribution lying at or below x.
The Beta distribution describes a proportion — a success rate, a share, a probability you are uncertain about — and this is its cumulative function. Through it come the tail probabilities of Student’s t, the F distribution and the binomial, which is why it turns up far more often than its name suggests.
Regularized is stated rather than implied: this is the ratio in [0, 1],
not the unnormalised integral B(x; a, b). Libraries disagree on which the
bare name means, and regularizedIncompleteGamma spells it out for the
same reason.
Relative error is a few ulps for ordinary parameters and stays within a few dozen for extreme ones.
O(maxIterations) continued-fraction steps in the worst case, and far fewer
in practice; O(1) memory.
Parameters
Section titled “Parameters”number
First shape parameter, positive.
number
Second shape parameter, positive.
number
Point of evaluation, in [0, 1].
options?
Section titled “options?”Termination criteria; tolerance is relative and defaults to
Number.EPSILON, maxIterations to 1000.
Returns
Section titled “Returns”number
Iₓ(a, b), in [0, 1].
Example
Section titled “Example” regularizedIncompleteBeta(2, 3, 0.5); // 0.6875 regularizedIncompleteBeta(0.5, 0.5, 0.5); // 0.49999999999999944 — the arcsine law ```;
## Throws
When `a ≤ 0`, `b ≤ 0`, or `x` is outside `[0, 1]`.
## Throws
When the continued fraction met no tolerance.
## See
- [inverseRegularizedIncompleteBeta](inverseRegularizedIncompleteBeta.md) to go the other way. - [Incomplete gamma and beta](https://anthochamp.pages.grenadine.io/node-essentials/topics/math/functions/incomplete-gamma-beta/)