dens<-function(x,kernel="Epanechnikov",lambda=1,npt=100)
{
 r<-max(x)-min(x)
 xmax<-max(x)+.1*r
 xmin<-min(x)-.1*r
 n<-length(x)
 xgrid<-seq(from=xmin,to=xmax,length=npt)
 myy<-NULL
 for (i in 1:npt)
 {
  bm<-(rep(xgrid[i],n)-x)/lambda
  if(kernel=="Gaussian")
   bm<-dnorm(bm)
#  The other kernels in use are defined only on [-1,1], and are zero at 1.
#  This command will zero out everything not in the interval [-1,1]
  else {
   bm<-ifelse(abs(bm)>1,1,bm)
   if(kernel=="Epanechnikov")
    bm<-3*(1-bm^2)/4
   else if(kernel=="Triangular")
    bm<-1-abs(bm)
   else if(kernel=="Biweight")
    bm<-15*(1-bm^2)^2/16
   else
    return("Unknown kernel\n")
  }
 myy<-c(myy,sum(bm*x))
 }
 plot(xgrid, myy,type="l",ylab=" ",   xlab=" ")
 cbind(xgrid,myy)
}