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# extval_gumbel

Calculates the probability (PDF) and cumulative (CDF) distribution functions of the Gumbel (Type I) distribution function given the scale and location parameters.

Available in version 6.4.0 and later.

## Prototype

```	function extval_gumbel (
x          : numeric,
scale  [*] : numeric,
center [*] : numeric,
opt    [1] : integer
)

return_val [ variable of type list containing 2 variables [/ PDF, CDF /]
```

## Arguments

x

A numeric array.

scale

One dimensional array containing the scale parameter(s). Must be the same size as shape.

center

One dimensional array containing the center (aka, location) parameter(s). Must be the same size as scale.

opt

Currently, not used. Set to zero.

## Return value

A variable of type 'list.' The list contains two variables: the PDF and the CDF. See Example(s).

## Description

Use the equations associated with the Gumbel distribution to derive the associated PDF(s) and CDF(s).

## Examples

Example 1

See plots at Example 2 of the Extreme Value Applications page.

```   N      =  100
xMin   = -10.0
xMax   =  20
x      = fspan(xMin,xMax,N)

scale  = (/2.0, 2.0, 3.0, 4, 6/)
center = (/0.5,  1 , 1.5, 3, 3/)
nscl   = dimsizes( scale )

; -- Gumbel: Type I, Max

pdfcdf = extval_gumbel(x, center, scale,  1) ; minmax= 1
pdf    = pdfcdf[0]                      ; extract from list for convenience
cdf    = pdfcdf[1]

printVarSummary(pdf)
print("==========")
printVarSummary(cdf)
print("==========")

; -- Gumbel: Type I, Min

PDFCDF = extval_gumbel(x, center, scale, -1)  ;  minmax=-1
PDF    = PDFCDF[0]                      ; extract from list for convenience
CDF    = PDFCDF[1]

printVarSummary(PDF)
print("==========")
printVarSummary(CDF)
print("==========")

```
The (edited) output is:
```     Variable: pdf
Type: float
Total Size: 2000 bytes
500 values
Number of Dimensions: 2
Dimensions and sizes:   [5] x [100]
Coordinates:
Number Of Attributes: 4
_FillValue :  9.96921e+36
long_name :   Gumbel: Extreme Value Type I: Maxima; PDF
center :   (  2,  2,  3,  4,  6 )
scale :    ( 0.5,  1, 1.5,  3,  3 )
(0)     ==========

Variable: cdf
Type: float
Total Size: 2000 bytes
500 values
Number of Dimensions: 2
Dimensions and sizes:   [5] x [100]
Coordinates:
Number Of Attributes: 2
_FillValue :  9.96921e+36
long_name :   Gumbel: Extreme Value Type I: Maxima; CDF
center :   (  2,  2,  3,  4,  6 )
scale :    ( 0.5,  1, 1.5,  3,  3 )
(0)     ==========

Variable: PDF
Type: float
Total Size: 2000 bytes
500 values
Number of Dimensions: 2
Dimensions and sizes:   [5] x [100]
Coordinates:
Number Of Attributes: 4
_FillValue :  9.96921e+36
long_name :   Gumbel: Extreme Value Type I: Minima; PDF
center :   (  2,  2,  3,  4,  6 )
scale :    ( 0.5,  1, 1.5,  3,  3 )
(0)     ==========

Variable: CDF
Type: float
Total Size: 2000 bytes
500 values
Number of Dimensions: 2
Dimensions and sizes:   [5] x [100]
Coordinates:
Number Of Attributes: 2
_FillValue :  9.96921e+36
long_name :   Gumbel: Extreme Value Type I: Minima; CDF
center :   (  2,  2,  3,  4,  6 )
scale :    ( 0.5,  1, 1.5,  3,  3 )

```