Inverse incomplete beta function

This calculator calculates the inverse incomplete regularized beta function Ix^-1(a,b).

To perform the calculation, enter the beta parameters a,b and y, then click the 'Calculate' button.

The parameters a and b must be >0. The value of y is 0 <= x <= 1.

Formulas for the beta functions

Incomplete beta function

\(\displaystyle B_x(a,b)=\int_0^xt^{a-1}(1-t)^{b-1}dt,\)    \(\displaystyle Re(a), Re(b)>0,\,\,\,1≥x≥0\)

Incomplete regularized beta function

\(\displaystyle I_x(a,b)=\frac{B_x(a,b}{B(a,b)} \)

\(\displaystyle I_x(a,b)+I_{1-x}(b,a)=1 \)