# Maximum normalniho rozdeleni
####################################
plot(dnorm,-5,5,ylim=c(0,1.2)) #hustota normalniho rozdeleni N(0,1)

# hustota maxima nahodneho vyberu z N(0,1) o rozsahu n
ind=c(2,5,10,100,1000)
for (i in ind){
f=function(x){
f=i*dnorm(x)*pnorm(x)^(i-1)}
plot(f,-5,5,add=T,col=i)
}
legend("topleft",legend=c(1,ind),col=c(1,ind),lty=1,lwd=2,title="n")

####################################
# Maximum exponencialniho rozdeleni
####################################
plot(dexp,0,15,ylim=c(0,1)) #hustota exponencialniho rozdeleni Ex(1)

# hustota maxima nahodneho vyberu z Ex(1) o rozsahu n
ind=c(2,5,10,100,1000,10000)
for (i in ind){
f=function(x){
f=i*dexp(x)*pexp(x)^(i-1)}
plot(f,-5,15,add=T,col=i)
}
legend("topright",legend=c(1,ind),col=c(1,ind),lty=1,lwd=2,title="n")

####################################
# Maximum exponencialniho - standardizovane
####################################
plot(dexp,-5,5,ylim=c(0,1))
col=2:7
ind=c(2,5,10,100,1000,10000)
for (i in col){
n=ind[i-1]
f=function(x){
f=n*dexp(x+log(n))*pexp(x+log(n))^(n-1)}
plot(f,-5,5,add=T,col=i)
}

g=function(x){
g=exp(-(x+exp(-x)))
}

plot(g,-5,20,add=T,col=8)

legend("topleft",legend=c(1,ind,Inf),col=1:8,lty=1,lwd=2,title="n")

########################################
# Rozdeleni extremnich hodnot
########################################
library(evd)
curve(dgumbel,-10,10,col=1,ylab="g0(x)",main="Gumbel distribution")
abline(v=0)

ind=c(-5,-1,3,7)
col=2:5
for (i in col){
curve(dgumbel(x,loc=ind[i-1]),-10,10,col=i,add=T)}
legend("topleft",legend=c(0,ind),col=c(1,col),lty=1,lwd=2,title=expression(mu))


curve(dgumbel,-10,10,col=1,ylab="g0(x)",main="Gumbel distribution")
ind=c(2,3,5,10)
col=2:5
for (i in col){
curve(dgumbel(x,scale=ind[i-1]),-10,10,col=i,add=T)}
legend("topright",legend=c(1,ind),col=c(1,col),lty=1,lwd=2,title=expression(sigma))
abline(v=0)

curve(dfrechet(x,shape=10),0,5,col=10,ylab="g1(x)",main="Frechet distribution")
ind=c(1,3,5,8)
for (i in ind){
curve(dfrechet(x,shape=i),0,5,col=i,add=T)}
legend("topright",legend=c(ind,10),col=c(ind,10),lty=1,lwd=2,title=expression(alpha))


curve(drweibull(x,shape=5),-5,0,col=5,ylab="g2(x)",main="Weibull distribution")
ind=c(1,2,3,4)
for (i in ind){
curve(drweibull(x,shape=i),-5,0,col=i,add=T)}
legend("topleft",legend=c(-ind,-5),col=c(ind,5),lty=1,lwd=2,title=expression(alpha))


curve(dgev(x,shape=0),-7,7,col=1,ylim=c(0,1),ylab="g(x)",main="GEV distribution")
ind=c(-1,-0.5,0.5,1)
col=2:5
for (i in col){
curve(dgev(x,shape=ind[i-1]),-7,7,col=i,add=T)}
abline(v=0)
legend("topright",legend=c(0,ind),col=c(1,col),lty=1,lwd=2,title=expression(gamma))