Sfun.BetaIncomplete Method

Returns the incomplete Beta function ratio.

public static double BetaIncomplete(
   double x,
   double p,
   double q
);

Parameters

x: A double value specifying the upper limit of integration It must be in the interval [0,1] inclusive.
p: A double value specifying the first Beta parameter. It must be positive.
q: A double value specifying the second Beta parameter. It must be positive.

Return Value

A double value specifying the incomplete Beta function ratio.

Remarks

The incomplete beta function is defined to be

$I_x (p,\,\,q) = {{\beta _x (p,\,\,q)} \over {\beta (p,\,\,q)}} = {1 \over {\beta (p,\,\,q)}}\int_0^x {t^{p - 1} } (1 - t)^{q - 1} dt\,\,{\rm{for}}\,\,0 \le x \le 1,\,p > 0,\,q > 0$

See Beta for the definition of $\beta \left( {p,\,q} \right)$ .

The parameters p and q must both be greater than zero. The argument x must lie in the range 0 to 1. The incomplete beta function can underflow for sufficiently small x and large p; however, this underflow is not reported as an error. Instead, the value zero is returned as the function value.

The method BetaIncomplete is based on the work of Bosten and Battiste (1974).

Sfun.BetaIncomplete Method

Parameters

Return Value

Remarks

See Also