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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

load "$NCARG_ROOT/lib/ncarg/nclscripts/csm/extval.ncl"

	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).

See Also

Extreme Value functions

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 )