extval_frechet
Calculates the probability (PDF) and cumulative (CDF) distribution functions of the Frechet Type II distribution given the shape, scale and location parameters.
Available in version 6.4.0 and later.
Prototype
function extval_frechet ( x : numeric, shape [*] : numeric, scale [*] : numeric, center [*] : numeric, opt [1] : integer ) return_val [ variable of type list containing 2 variables [/ PDF, CDF /]
Arguments
xA numeric array.
shapeOne dimensional array containing the shape parameter(s).
scaleOne dimensional array containing the scale parameter(s). Must be the same size as shape.
centerOne dimensional array containing the center (aka, location) parameter(s). Must be the same size as shape.
optCurrently, 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 Frechet distribution to derive the associated PDFs and CDFs.
See Also
extval_mlegev, extval_gev, extval_gumbel, extval_weibull, extval_recurrence_table
Examples
Example 1
See plots at Example 3 of the Extreme Value Applications page.
N = 1000 xMin = 0.05 xMax = 5.5 x = fspan(xMin,xMax,N) shape = (/0.5, 1.0, 2.0, 3.0, 1.0, 2.0, 3.0/) scale = (/1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0/) center = (/0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0/) ; Generate PDF and GDF distribution pdfcdf = extval_frechet(x, shape, scale, center, 0) ; return a variable of type 'list' pdf = pdfcdf[0] ; explicitly extract the 2 returned variables (for convenience only). cdf = pdfcdf[1] delete(pdfcdf) ; not necessary printVarSummary(pdf) printVarSummary(cdf)The (edited) ourput is:
Variable: pdf Type: float Total Size: 28000 bytes 7000 values Number of Dimensions: 2 Dimensions and sizes: [7] x [1000] Coordinates: Number Of Attributes: 4 _FillValue : 9.96921e+36 long_name : PDF Frechet: Extreme Value Type II: Maxima shape : ( 0.5, 1, 2, 3, 1, 2, 3 ) scale : ( 1, 1, 1, 1, 2, 2, 2 ) (0) --- Variable: cdf Type: float Total Size: 28000 bytes 7000 values Number of Dimensions: 2 Dimensions and sizes: [7] x [1000] Coordinates: Number Of Attributes: 4 _FillValue : 9.96921e+36 long_name : CDF: Frechet: Extreme Value Type II: Maxima shape : ( 0.5, 1, 2, 3, 1, 2, 3 ) scale : ( 1, 1, 1, 1, 2, 2, 2 )