<< Extreme Value Extreme Value distfun_evinv >>

distfun >> distfun > Extreme Value > distfun_evcdf

distfun_evcdf

Extreme value (Gumbel) CDF

Calling Sequence

p=distfun_evcdf(x,mu,sigma)
p=distfun_evcdf(x,mu,sigma,lowertail)

Parameters

x :

a matrix of doubles, the outcome

mu :

a matrix of doubles, the location

sigma :

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

lowertail :

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).

p :

a matrix of doubles, the probability.

Description

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.

Examples

// 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

Authors


Report an issue
<< Extreme Value Extreme Value distfun_evinv >>