<< distfun_evrnd Extreme Value Exponential >>

Distfun >> Distfun > Extreme Value > distfun_evstat

distfun_evstat

Extreme value (Gumbel) mean and variance

Calling Sequence

M = distfun_evstat ( mu , sigma )
[M,V] = distfun_evstat ( mu , sigma )

Parameters

mu :

a matrix of doubles, the location

sigma :

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

M :

a matrix of doubles, the mean

V :

a matrix of doubles, the variance

Description

Computes statistics from the Extreme value (Gumbel) distribution. This is the minimum Gumbel distribution.

The mean and variance of the Extreme value (Gumbel) distribution are

where

z=dlgamma(1)=-0.5772157...

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

Examples

[M,V]=distfun_evstat(5,2)
me = 3.8455687;
ve = 6.5797363;

mu=0.5;
sigma=2.0;
[M,V]=distfun_evstat(mu,sigma);
R=distfun_evrnd(mu,sigma,1000,1000);
m=mean(R,"r");
v=variance(R,"r");
//
scf();
xtitle("Estimate of mean","Mean","Frequency")
histplot(11,m);
plot([M,M],[0,5])
legend(["Data","Exact"]);
//
scf();
xtitle("Estimate of variance","Variance","Frequency")
histplot(11,v);
plot([V,V],[0,1])
legend(["Data","Exact"]);

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