GAMMAINC

The regularized lower incomplete gamma function gives the normalized lower-tail accumulation of the gamma kernel and is commonly used in cumulative gamma-distribution calculations.

It is defined by:

P(a,x)=\frac{1}{\Gamma(a)}\int_0^x t^{a-1}e^{-t}\,dt

for a>0 and x\ge 0. This wrapper returns the lower regularized value in [0,1].

Excel Usage

=GAMMAINC(a, x)

a (float, required): Positive shape parameter.
x (float, required): Nonnegative argument.

Returns (float): Regularized lower incomplete gamma value.

Example 1: Lower incomplete gamma at origin

Inputs:

a	x
0.5	0

Excel formula:

=GAMMAINC(0.5, 0)

Expected output:

0

Example 2: Lower incomplete gamma at one

Inputs:

a	x
0.5	1

Excel formula:

=GAMMAINC(0.5, 1)

Expected output:

0.842701

Example 3: Lower incomplete gamma at moderate input

Inputs:

a	x
2	3

Excel formula:

=GAMMAINC(2, 3)

Expected output:

0.800852

Example 4: Lower incomplete gamma near saturation

Inputs:

a	x
0.5	10

Excel formula:

=GAMMAINC(0.5, 10)

Expected output:

0.999992

Python Code

from scipy.special import gammainc as scipy_gammainc

def gammainc(a, x):
    """
    Compute the regularized lower incomplete gamma function.

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

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

    Args:
        a (float): Positive shape parameter.
        x (float): Nonnegative argument.

    Returns:
        float: Regularized lower incomplete gamma value.
    """
    try:
        if a <= 0:
            return "Error: a must be positive"
        if x < 0:
            return "Error: x must be nonnegative"
        return float(scipy_gammainc(a, x))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

a *

Positive shape parameter.

x *

Nonnegative argument.