Double BetaIncomplete(Double x, Double a, Double b)
Regularized incomplete beta function.
| # | Name | Description |
|---|---|---|
| 1 | x | upper integration limit |
| 2 | real on the closed interval [0,1]. | |
| 3 | a | first shape parameter |
| 4 | real positive. | |
| 5 | b | second shape parameter |
| 6 | real positive. |
Returns: Double - 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 Dew.Math.Units.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