GAMMAINCC

The regularized upper incomplete gamma function gives the normalized upper-tail accumulation of the gamma kernel and complements the lower regularized form.

It is defined by:

Q(a,x)=\frac{1}{\Gamma(a)}\int_x^{\infty} t^{a-1}e^{-t}\,dt

for a>0 and x\ge 0. It satisfies P(a,x)+Q(a,x)=1 with the lower function P.

Excel Usage

=GAMMAINCC(a, x)

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

Returns (float): Regularized upper incomplete gamma value.

Example 1: Upper incomplete gamma at origin

Inputs:

a	x
0.5	0

Excel formula:

=GAMMAINCC(0.5, 0)

Expected output:

1

Example 2: Upper incomplete gamma at one

Inputs:

a	x
0.5	1

Excel formula:

=GAMMAINCC(0.5, 1)

Expected output:

0.157299

Example 3: Upper incomplete gamma at moderate input

Inputs:

a	x
2	3

Excel formula:

=GAMMAINCC(2, 3)

Expected output:

0.199148

Example 4: Upper incomplete gamma near zero tail

Inputs:

a	x
0.5	10

Excel formula:

=GAMMAINCC(0.5, 10)

Expected output:

0.00000774422

Python Code

from scipy.special import gammaincc as scipy_gammaincc

def gammaincc(a, x):
    """
    Compute the regularized upper incomplete gamma function.

    See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.gammaincc.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 upper 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_gammaincc(a, x))
    except Exception as e:
        return f"Error: {str(e)}"

Online Calculator

a *

Positive shape parameter.

x *

Nonnegative argument.