NCL Home > Documentation > Functions > Cumulative distribution functions

# cdfgam_x

Calculates the upper limit of integration of a cumulative gamma distribution function.

## Prototype

```	function cdfgam_x (
p      : numeric,
shape  : numeric,
scale  : numeric
)

return_val  :  numeric
```

## Arguments

p

A multi-dimensional array or scalar value equal to the integral from 0 to return_val [0,1].

shape

A multi-dimensional array or scalar value equal to the shape parameter of the gamma density (shape > 0.0)

scale

A multi-dimensional array or scalar value equal to the scale parameter of the gamma density (scale > 0.0)

## Return value

A array of the same size as p. Double if any of the input arguments are double, float otherwise.

## Description

Calculates the upper limit of integration of a cumulative gamma distribution function.

This is equivalent to Matlab's gaminv function but the scale argument must be be inverted.

The source code is from source routine "CDFGAM" from DCDFLIB (Double precision Cumulative Distribution Function LIBrary)

## Examples

Example 1

```     p     = 0.95
shape = 3.0
scale = 1.0

x = cdfgam_x(p,shape,scale)
print("x="+x)               ; x = 6.29579
```

Example 2

```     q = ispan(1,5,1)
r = ispan(6,10,1)
P = cdfgam_p(q, q, 1.0/r)  ; NOTE the inverse
print(P)                    ; P=> 0.1535183, 0.03381491, 0.006652214
;     0.001142394, 0.000172115

X = cdfgam_x(P,q,1./r)      ; X=> 1, 2, 3, 4, 5
```