double BetaIncomplete(double x, double a, double b);
Regularized incomplete beta function.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | x | double | upper integration limit; real on the closed interval [0,1]. |
| 2 | a | double | first shape parameter; real positive. |
| 3 | b | double | second shape parameter; real positive. |
Returns: the regularized incomplete beta function for given parameters x, a and b.
Remarks:
The regularized incomplete beta function is defined by:
I_x(a,b)=1/B(a,b)integral _0^x t^(a-1)(1-t)^(b-1) dt ,
where is the Probabilities::Beta function. It is evaluated through a continued-fraction expansion and satisfies I_x(a,b)=1-I_(1-x)(b,a).
Domain: x in [0,1], a > 0, b > 0. Defined behavior: returns 0 at x=0 and 1 at x=1; the result lies in and is monotone non-decreasing in x. Returns 0 for out-of-domain parameters (a <= 0, b <= 0, x < 0 or x > 1), and returns NAN when any argument is NAN.
See Also: Probabilities::Beta
Declared in Dew::Math::Units::Probabilities · Dew.Math/Units.Probabilities.h · Cross-compiler