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Distfun >> Distfun > Extreme Value > distfun_evpdf

distfun_evpdf

Extreme value (Gumbel) PDF

Calling Sequence

y=distfun_evpdf(x,mu,sigma)

Parameters

x :

a matrix of doubles, the outcome

mu :

a matrix of doubles, the location

sigma :

a matrix of doubles, the scale. sigma>0.

y :

a matrix of doubles, the density

Description

Computes the probability distribution function of the Extreme value (Gumbel) function. This is the minimum Gumbel distribution.

Any scalar input argument is expanded to a matrix of doubles of the same size as the other input arguments.

The function definition is:

where

To get the max-Gumbel PDF:

y = distfun_evpdf(-x,-mu,sigma)

Examples

computed = distfun_evpdf ( [-1 1] , 0 , 1 )
expected = [0.2546464 0.1793741];

// Plot the Gumbel PDF
N=1000;
x=linspace(-20,5,N);
y1= distfun_evpdf(x,-0.5,2.);
y2= distfun_evpdf(x,-1.0,2.);
y3= distfun_evpdf(x,-1.5,3.);
y4= distfun_evpdf(x,-3.0,4.);
scf();
xtitle("Gumbel","x","Density");
plot(x,y1,"r-")
plot(x,y2,"g-")
plot(x,y3,"b-")
plot(x,y4,"c-")
leg(1)="$\mu=-0.5,\beta=2.0$";
leg(2)="$\mu=-1.0,\beta=2.0$";
leg(3)="$\mu=-1.5,\beta=3.0$";
leg(4)="$\mu=-3.0,\beta=4.0$";
legend(leg,"in_upper_left");

Bibliography

http://en.wikipedia.org/wiki/Gumbel_distribution

NIST/SEMATECH e-Handbook of Statistical Methods,

http://www.itl.nist.gov/div898/handbook/

http://www.itl.nist.gov/div898/handbook/eda/section3/eda366g.htm

Authors


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