Add density lines to histogram and cumulative histogram

Question

I want to add density curve to histogram and cumulative histogram, like this:

Here is as far I can go:

hist.cum <- function(x, plot=TRUE, ...){
  h <- hist(x, plot=FALSE, ...)
  h$counts <- cumsum(h$counts)
  h$density <- cumsum(h$density)
  h$itensities <- cumsum(h$itensities)
  if(plot)
    plot(h)
  h
}
 x <- rnorm(100, 15, 5)
hist.cum(x)
 hist(x, add=TRUE, col="lightseagreen")

 #
lines (density(x), add = TRUE, col="red")

Answer 1

Offered without explanation:

## Make some sample data
x <- sample(0:30, 200, replace=T, prob=15 - abs(15 - 0:30))

## Calculate and plot the two histograms
hcum <- h <- hist(x, plot=FALSE)
hcum$counts <- cumsum(hcum$counts)
plot(hcum, main="")
plot(h, add=T, col="grey")

## Plot the density and cumulative density
d <- density(x)
lines(x = d$x, y = d$y * length(x) * diff(h$breaks)[1], lwd = 2)
lines(x = d$x, y = cumsum(d$y)/max(cumsum(d$y)) * length(x), lwd = 2)