Extreme value (Gumbel) CDF
p=distfun_evcdf(x,mu,sigma) p=distfun_evcdf(x,mu,sigma,lowertail)
a matrix of doubles, the outcome
a matrix of doubles, the location
a matrix of doubles, the scale. sigma>0.
a 1-by-1 matrix of booleans, the tail (default lowertail=%t). If lowertail is true (the default), then considers P(X<=x) otherwise P(X>x).
a matrix of doubles, the probability.
Computes the cumulated 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.
// Test expanded arguments computed = distfun_evcdf([1 2 3],1,2) expected = [0.6321206 0.8077044 0.9340120] // Plot the Gumbel CDF N=1000; x=linspace(-20,5,N); p1= distfun_evcdf(x,-0.5,2.,%t); p2= distfun_evcdf(x,-1.0,2.,%t); p3= distfun_evcdf(x,-1.5,3.,%t); p4= distfun_evcdf(x,-3.0,4.,%t); scf(); xtitle("Gumbel","x","P(X<x)"); plot(x,p1,"r-") plot(x,p2,"g-") plot(x,p3,"b-") plot(x,p4,"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"); p=distfun_evcdf(1,0.5,2.,%t) q=distfun_evcdf(1,0.5,2.,%f) p+q | ![]() | ![]() |