and is the same as the the cumulative distribution function.
The domain of definition is 0 <= x <= 1. In this
implementation a and b are restricted to positive values.
The integral from x to 1 may be obtained by the symmetry
relation
betaIncompleteCompl(a, b, x ) = betaIncomplete( b, a, 1-x )
The integral is evaluated by a continued fraction expansion
or, when b*x is small, by a power series.
Incomplete beta integral
Returns incomplete beta integral of the arguments, evaluated from zero to x. The regularized incomplete beta function is defined as
betaIncomplete(a, b, x) = Γ(a+b)/(Γ(a) Γ(b)) * $(INTEGRATE 0, x) ta-1(1-t)b-1 dt
and is the same as the the cumulative distribution function.
The domain of definition is 0 <= x <= 1. In this implementation a and b are restricted to positive values. The integral from x to 1 may be obtained by the symmetry relation
betaIncompleteCompl(a, b, x ) = betaIncomplete( b, a, 1-x )
The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.