| a | x | gammaIncompleteCompl(a, x) |
|---|---|---|
| negative | NaN | |
| < 0 | NaN | |
| positive | 0 | 1 |
| positive | ∞ | 0 |
| +0 | ≥ 0 | 0 |
| ∞ | (0, ∞) | 1 |
gammaIncompleteCompl
fn
real gammaIncompleteCompl(real a, real x ) pure nothrow @safe @nogcRegularized upper incomplete gamma function Q(a,x)
Mathematically, Q(a,x) = Γ(a,x)/Γ(a), where Γ(a,x) is the upper incomplete gamma function, Γ(a,x) = ∫x∞ta-1e-tdt, a ≥ 0, and x ≥ 0. Note that P(a,x) + Q(a,x) = 1 or Q(a,x) = 1 - P(a,x), so Q is the complement of P.
Parameters
a | the shape parameter, must be positive |
x | the fraction of integration completion from above, must be non-negative |
Returns
It returns Q(a,x), an element of [0,1].
See Also
gamma and gammaIncomplete