inverseRegularizedIncompleteBeta
inverseRegularizedIncompleteBeta(
a,b,p,options?):number
Defined in: packages/math-analysis/src/inverse-regularized-incomplete-beta.ts:74
The inverse of regularizedIncompleteBeta in its third argument: the
x at which Iₓ(a, b) equals p.
The quantile function of a Beta(a, b) distribution, and what the Beta,
F and StudentT quantiles in @ac-kit/math-stats are built on. Use it to
turn a confidence level into a critical value, or a percentile into the
proportion that sits there.
Accurate to within a few ulps in the round trip: feeding the result back
through Iₓ returns the p you started from to about 1e-15 relative.
O(maxIterations) evaluations of Iₓ in the worst case; three or four in
practice, because convergence is cubic. O(1) memory.
Parameters
Section titled “Parameters”number
First shape parameter, positive.
number
Second shape parameter, positive.
number
Probability, in [0, 1].
options?
Section titled “options?”Termination criteria; tolerance is compared against the
relative size of the refinement step and defaults to Number.EPSILON,
maxIterations to 100.
Returns
Section titled “Returns”number
The x with Iₓ(a, b) = p; 0 at p = 0 and 1 at p = 1.
Example
Section titled “Example” inverseRegularizedIncompleteBeta(2, 3, 0.5); // 0.38572756813238934 ```;
## Throws
When `a ≤ 0`, `b ≤ 0`, or `p` is outside `[0, 1]`.
## See
- [regularizedIncompleteBeta](regularizedIncompleteBeta.md) for the forward direction. - [Incomplete gamma and beta](https://anthochamp.pages.grenadine.io/node-essentials/topics/math/functions/incomplete-gamma-beta/)