set.seed(1234)
n=30
X=rnorm(n) # data


# (a) vyberovy prumer
i=1 # IF pro prvni pozorovani

IF=function(x){
IF=n*(mean(c(X[-i],x))-mean(X))
return(IF)
}

ind=seq(-10,10, by=0.01) #graf vykreslime na mrizce od -10 do 10


plot(Vectorize(IF)(ind)~ind, type="l",xlab="x",ylab="EIF(x)")

#jina definice
IF2=function(x){
IF2=(n+1)*(mean(c(X,x))-mean(X))
return(IF2)
}

plot(Vectorize(IF2)(ind)~ind, type="l",xlab="x",ylab="EIF(x)")



# (b) median

IF=function(x){
IF=n*(median(c(X[-i],x))-median(X))
return(IF)
}

plot(Vectorize(IF)(ind)~ind, type="l",xlab="x",ylab="EIF(x)")


# (c) useknuty prumer

IF=function(x){
IF=n*(mean(c(X[-i],x),trim=0.1)-mean(X,trim=0.1))
return(IF)
}

plot(Vectorize(IF)(ind)~ind, type="l",xlab="x",ylab="EIF(x)")


# (d) winsorizovany prumer
library(psych)

IF=function(x){
IF=n*(winsor.mean(c(X[-1],x),0.1)-winsor.mean(X,0.1))
return(IF)
}

plot(Vectorize(IF)(ind)~ind, type="l",xlab="x",ylab="EIF(x)")