real betaIncompleteCompl(real a, real b, real x) pure nothrow @safe @nogcRegularized incomplete beta function complement IC, x(a,b)
Mathematically, if a ≥ 0, b ≥ 0, and 0 ≤ x ≤ 1, then IC, x(a,b) = ∫x1ta-1(1-t)b-1dt/B(a,b) where B is the beta function. It is also the complement of the cumulative distribution function of the beta distribution. It can be shown that IC, x(a,b) = I, 1-x(b,a).
betaIncompleteCompl(a, b, x) evaluates IC, x(a,b).
a | the first argument of B, must be positive |
b | the second argument of B, must be positive |
x | the fraction of integration completion from above, 0 ≤ x ≤ 1 |
| a | b | x | betaIncompleteCompl(a, b, x) |
|---|---|---|---|
| negative | b | x | NaN |
| a | negative | x | NaN |
| a | b | < 0 | NaN |
| a | b | ≥ 1 | NaN |
| +0 | +0 | (0,1) | NaN |
| ∞ | ∞ | (0,1) | NaN |
If one or more of the input parameters are NaN, the one with the largest payload is returned. For equal payloads but with possibly different signs, the order of preference is x, a, b.