BETAINCINV

This function solves for the unit-interval argument x in the regularized incomplete beta relation for fixed positive parameters a and b.

It finds x such that:

y = I_x(a,b)

where I_x(a,b) is the regularized incomplete beta function. The output lies in [0,1] when inputs are in-domain.

Excel Usage

=BETAINCINV(a, b, y)

• a (float, required): First positive shape parameter.
• b (float, required): Second positive shape parameter.
• y (float, required): Regularized incomplete beta target value in the unit interval.

Returns (float): Unit-interval x value satisfying the inverse regularized incomplete beta equation.

Example 1: Inverse regularized incomplete beta at central probability

Inputs:

a	b	y
1.2	3.1	0.5

Excel formula:

=BETAINCINV(1.2, 3.1, 0.5)

Expected output:

0.242835

Example 2: Inverse regularized incomplete beta at low probability

Inputs:

a	b	y
2	5	0.1

Excel formula:

=BETAINCINV(2, 5, 0.1)

Expected output:

0.0925953

Example 3: Inverse regularized incomplete beta at high probability

Inputs:

a	b	y
7.5	0.4	0.8

Excel formula:

=BETAINCINV(7.5, 0.4, 0.8)

Expected output:

0.998143

Example 4: Inverse regularized incomplete beta at zero

Inputs:

a	b	y
2	2	0

Excel formula:

=BETAINCINV(2, 2, 0)

Expected output:

0

Python Code

from scipy.special import betaincinv as scipy_betaincinv

def betaincinv(a, b, y):
    """
    Invert the regularized incomplete beta function with respect to x.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.betaincinv.html

    This example function is provided as-is without any representation of accuracy.

    Args:
        a (float): First positive shape parameter.
        b (float): Second positive shape parameter.
        y (float): Regularized incomplete beta target value in the unit interval.

    Returns:
        float: Unit-interval x value satisfying the inverse regularized incomplete beta equation.
    """
    try:
        if a <= 0 or b <= 0:
            return "Error: a and b must be positive"
        if y < 0 or y > 1:
            return "Error: y must be between 0 and 1"
        return float(scipy_betaincinv(a, b, y))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

a *

First positive shape parameter.

b *

Second positive shape parameter.

y *

Regularized incomplete beta target value in the unit interval.