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, bfloat \in \Rset^*_+
xfloat
tailbool, optional

By default, tail is False.

Returns
resultfloat

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

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

See also

SpecFunc_IncompleteBeta, SpecFunc_Beta