library(nortest)

# ukol 1

#nagenerovane datove soubory
n=30
set.seed(1235)
x1=runif(n,-5,5)
x2=rlogis(n)
x3=c(rexp(15,3),-rexp(15,3))
x3=sample(x3,n)
x4=rt(n,3)
x5=rnorm(n)
x6=rcauchy(n)
x7=rchisq(n,5)-5
x8=log(rexp(n,1))
x9=c(rnorm(n-3),rcauchy(3))
x9=sample(x9,n)
x10=c(rnorm(n-2),-3,3)
x10=sample(x10,n)

#(a)
par(mfrow=c(1,2))
hist(x1,freq=FALSE)
curve(dnorm(x,mean=mean(x1),sd=sd(x1)),col=2,add=TRUE)
plot(density(x1),ylim=c(0,0.15))
curve(dnorm(x,mean=mean(x1),sd=sd(x1)),col=2,add=TRUE)

boxplot(x1)

#(b)
qqnorm(x1)
qqline(x1)

#(c)
plot(ppoints(n,0),pnorm((sort(x1) - mean(x1))/sd(x1)))
abline(0,1)

#(d)
shapiro.test(x1)
lillie.test(x1)
pearson.test(x1)


# ukol 2

n=50

zam=0
zam2=0
zam3=0

pval=0
pval2=0
pval3=0

set.seed(1234)
for (i in 1:10000){
x=rnorm(n)
#x=rexp(n)
pval[i]=ks.test(x,"pnorm",0,1)$p.value
if (pval[i]<0.05) zam=zam+1

pval2[i]=ks.test(x,"pnorm",mean(x),sd(x))$p.value
if (pval2[i]<0.05) zam2=zam2+1

pval3[i]=lillie.test(x)$p.value
if (pval3[i]<0.05) zam3=zam3+1

}

par(mfrow=c(3,1))
hist(pval, main="Zname parametry")
hist(pval2, main="Odhadnute parametry")
hist(pval3, main="Lillieforsova varianta")

print(c("Empiricka hladina vyznamnosti pro K-S test se znamymi parametry v procentech:",zam/100))
print(c("Empiricka hladina vyznamnosti pro K-S test s odhadnutymi parametry v procentech:",zam2/100))
print(c("Empiricka hladina vyznamnosti pro Lillieforsovu variantu K-S testu v procentech:",zam3/100))