inverseRegularizedIncompleteGamma
inverseRegularizedIncompleteGamma(
a,p,options?):number
Defined in: packages/math-analysis/src/inverse-regularized-incomplete-gamma.ts:84
The inverse of regularizedIncompleteGamma in its second argument: the
x at which P(a, x) equals p.
This is the quantile function — the “which value sits at the 95th
percentile?” direction, where P answers “which percentile is this value
at?”. It is what the Gamma, ChiSquared and Poisson quantiles in
@ac-kit/math-stats are built on, and what turns a confidence level into a
critical value.
Accurate to within a few ulps in the round trip: feeding the result back
through P returns the p you started from to about 1e-15 relative.
O(maxIterations) evaluations of P or Q in the worst case; three or four
in practice, because convergence is cubic. O(1) memory.
Parameters
Section titled “Parameters”number
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 P(a, x) = p; 0 at p = 0 and Infinity at p = 1.
Example
Section titled “Example” const median = inverseRegularizedIncompleteGamma(3, 0.5); // 2.674060313723559 regularizedIncompleteGamma(3, median); // 0.4999999999999999 — back where we started ```;
## Throws
When `a ≤ 0` or `p` is outside `[0, 1]`.
## See
- [regularizedIncompleteGamma](regularizedIncompleteGamma.md) for the forward direction. - [Incomplete gamma and beta](https://anthochamp.pages.grenadine.io/node-essentials/topics/math/functions/incomplete-gamma-beta/)