betaIncomplete

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)) * ∫0^x t^a-1(1-t)^b-1 dt

and is the same as 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.