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gammaincinv - Inverse incomplete gamma function

Syntax

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

Description

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).

y = gammaincinv(x,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.

Definition

The lower incomplete gamma function is defined as:

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) , so gammaincinv(1,0) = 0.

See Also

gamma, gammainc, gammaln, psi

gamma, gammainc, gammaln

gca

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