SpecFunc_RegularizedIncompleteBeta

SpecFunc_RegularizedIncompleteBeta(a, b, x, tail=False)

Regularized incomplete Beta function.

\forall (a, b) > 0 \quad
\mathrm{I}(x; a, b) = \frac{\mathrm{B}(x; a, b)}{\mathrm{B}(a, b)}
                    = \frac{1}{\mathrm{B}(a, b)} \int_0^x t^{a-1}(1-t)^{b-1}\di{t}

with B(a, b) the Beta function and B(x; a, b) the incomplete Beta function.

Parameters:

a, b : float \in \Rset^*_+

x : float

tail : bool, optional

By default, tail is False.

Returns:

result : float

  • If tail is False: result = \mathrm{I}(x; a, b).
  • If tail is True: result = 1 - \mathrm{I}(x; a, b).