Extreme value (Gumbel) PDF
y=distfun_evpdf(x,mu,sigma)
a matrix of doubles, the outcome
a matrix of doubles, the location
a matrix of doubles, the scale. sigma>0.
a matrix of doubles, the density
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)
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"); | ![]() | ![]() |
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