# GAMMAINCINV

## Purpose:

Computes the inverse regularized incomplete gamma function.

## Syntax:

GAMMAINCINV(y, a, "tail")

y

-

A series or real number where 0 <= y <= 1.

a

-

A series or real number > 0, the exponential factor.

"tail"

-

Optional. A string, the upper or lower function flag.

 "lower": lower inverse incomplete gamma function (default) "upper": upper inverse incomplete gamma function

## Returns:

A scalar, series, or table.

## Example:

gammaincinv(gammainc(10, 2), 2)

returns 10.0.

## Example:

W1: gammainc(1..4, 0.5)

W2: gammaincinv(W1, 0.5)

returns the series {1, 2, 3, 4}

## Example:

gammaincinv(0..0.001..0.9, 3);

xlabel("y");ylabel("P^{-1}(3, y)");label("Inverse Incomplete Gamma Function")

returns 901 samples of P-1(3, y).

## Remarks:

The lower incomplete gamma function is defined as:

where a is the exponential factor and x is the integration limit.

GAMMAINC computes the regularized lower incomplete gamma function defined as:

where Q(a, x) is the regularized upper incomplete gamma function and Γ(a) is the gamma function implemented by GAMMA. Note that for GAMMAINC, the first argument is x, the integration limit.

GAMMAINCINV computes the inverse of GAMMAINC.

"Tail" specifies the upper or lower inverse regularized incomplete gamma function where "lower" computes the inverse of the integral from 0 to x and "upper" computes the inverse of the integral from x to ∞.

gammaincinv(1 - y, a) = gammaincinv(y,a,"upper").

If the inputs y and a are series, they must be of the same size.

BETAINC

BETAINCINV

EXPINT

GAMMA

GAMMAINC

GAMMAP

GAMMAQ