This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English version of the page.

Note: This page has been translated by MathWorks. Click here to see
To view all translated materials including this page, select Country from the country navigator on the bottom of this page.


Inverse incomplete gamma function


x = gammaincinv(y,a)
x = gammaincinv(y,a,tail)


x = gammaincinv(y,a) evaluates the inverse incomplete gamma function for corresponding elements of y and a, such that y = gammainc(x,a). The elements of y must be in the closed interval [0,1], and those of a must be nonnegative. y and a must be real and the same size (or either can be a scalar).

x = gammaincinv(y,a,tail) specifies the tail of the incomplete gamma function. Choices are 'lower' (the default) to use the integral from 0 to x, or 'upper' to use the integral from x to infinity.

These two choices are related as:

gammaincinv(y,a,'upper') = gammaincinv(1-y,a,'lower').

When y is close to 0, the 'upper' option provides a way to compute x more accurately than by subtracting y from 1.

More About

collapse all

Inverse Incomplete Gamma Function

The lower incomplete gamma function is defined as:


where Γ(a) is the gamma function, gamma(a). The upper incomplete gamma function is defined as:


gammaincinv computes the inverse of the incomplete gamma function with respect to the integration limit x using Newton's method.

For any a>0, as y approaches 1, gammaincinv(y,a) approaches infinity. For small x and a, gammainc(x,a)xa, so gammaincinv(1,0) = 0.


[1] Cody, J., An Overview of Software Development for Special Functions, Lecture Notes in Mathematics, 506, Numerical Analysis Dundee, G. A. Watson (ed.), Springer Verlag, Berlin, 1976.

[2] Abramowitz, M. and I.A. Stegun, Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series #55, Dover Publications, 1965, sec. 6.5.

Extended Capabilities

See Also

| | |