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Distfun >> Distfun > Extreme Value > distfun_evrnd

distfun_evrnd

Extreme value (Gumbel) random numbers

Calling Sequence

R = distfun_evrnd ( mu , sigma )
R = distfun_evrnd ( mu , sigma , [m,n] )
R = distfun_evrnd ( mu , sigma , m , n )

Parameters

mu :

a matrix of doubles, the average

sigma :

a matrix of doubles, the standard deviation. sigma>0.

m :

a 1-by-1 matrix of floating point integers, the number of rows of R

n :

a 1-by-1 matrix of floating point integers, the number of columns of R

R:

a matrix of doubles, the random numbers.

Description

Generates random variables from the Extreme value (Gumbel) distribution 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.

To get max-Gumbel random numbers:

y = -distfun_evrnd(-mu,sigma,m,n)

Examples

// Set the seed so as to always get the same results.
distfun_seedset(1);

// Test both mu and sigma expanded
computed = distfun_evrnd(1,2,[5,5])

// Plot Gumbel random numbers
N=1000;
x=linspace(-20,5,N);
y1=distfun_evpdf(x,0.5,2.);
R=distfun_evrnd(0.5,2,10000,1);
scf();
xtitle("Gumbel distribution","x","Density");
plot(x,y1)
histplot(20,R);
legend(["PDF","Data"],"in_upper_left");

// Compare with CDF
R=gsort(R,"g","i");
n=size(R,"*");
p=distfun_evcdf(R,0.5,2,%t);
scf();
plot(R,(1:n)'/n,"r-");
plot(R,p,"b-");
legend(["Empirical","CDF"],"in_upper_left");
xtitle("Gumbel distribution","x","P(X<x)");

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