Function std.mathspecial.betaIncomplete

Returns incomplete beta integral of the arguments, evaluated from zero to x. The regularized incomplete beta function is defined as

betaIncomplete(a, b, x) = &gamma;(a + b) / ( &gamma;(a) &gamma;(b) ) * 0, x t, a-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.

Prototype

real betaIncomplete(
  real a,
  real b,
  real x
) pure nothrow @nogc @safe;