rm(list=ls())

pdf("artificial.pdf")
set.seed(267)
n = 100
x = runif(n)
x = sort(x) 
sigma = sqrt(exp(sin(2*pi*x)))
eps = rnorm(n,0,sigma)
f = sin(pi*x)
y = f + eps
plot(x,y,pch=21,bg="pink",cex=1.4,ylab="",xlab="",xaxt="n",yaxt="n")
lines(x,f,lwd=4,col="purple")

q9 = qnorm(.9,f,sigma)
q1 = qnorm(.1,f,sigma)
lines(x,q9,col="red",lwd=4)
lines(x,q1,col="red",lwd=4)
title(ylab="y",line=1.5, cex.lab=1.8)
title(xlab="x", line=1.5, cex.lab=1.8)

dev.off()