Click or drag to resize

GammaRelatedBetaRegularized Method

BetaRegularized(x,a,b) calculates the double precision incomplete beta function ratio.
C#
Copy
            B_x(a,b)    Integral(0,x) t**(a-1) (1-t)**(b-1) dt
I_x(a,b) = --------- = ---------------------------------------
            B(a,b)                   B(a,b)

Namespace: Altaxo.Calc
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
Copy
public static double BetaRegularized(
	double x,
	double a,
	double b
)

Parameters

x  Double
upper limit of integration. x must be in (0,1) inclusive.
a  Double
first beta distribution parameter. a must be > 0.
b  Double
second beta distribution parameter. b must be > 0.

Return Value

Double
The incomplete beta function ratio.
Remarks
C#
Copy
The incomplete beta function ratio is the probability that a
random variable from a beta distribution having parameters a and b
will be less than or equal to x.
This is a translation from the Fortran version of DBETAI(X,PIN,QIN), SLATEC,
FNLIB, CATEGORY C7F, REVISION 920528, originally written by Fullerton W.,(LANL)
to C++.

References: Nancy E. Bosten and E. L. Battiste, Remark on Algorithm 179,
            Communications of the ACM 17, 3 (March 1974), pp. 156.

Calls   LnBeta(a,b)
See Also