Given a histogram obtained using given data points, how do I randomly sample from the distribution predicted by the histogram?
Any conceptual comment / R code would be welcome.
The idea is simply
For each observation in the new sample 1. choose a histogram bin according to the proportions of the original sample (treated as a discrete pmf) 2. sample uniformly from that bin-interval
For example in R:
#create an original histogram x=rgamma(200,4) xhist=hist(x,freq=FALSE) #sample from it samplesize=400 bins=with(xhist,sample(length(mids),samplesize,p=density,replace=TRUE)) # choose a bin result=runif(length(bins),xhist$breaks[bins],xhist$breaks[bins+1]) # sample a uniform in it hist(result,freq=FALSE,add=TRUE,bord=3)
Just for completeness, (since sampling from the kernel density estimate* is very simple):
repeat nsim times: sample (with replacement) a random observation from the data sample from the kernel, and add the previously sampled random observation
* note that some kernels - like fourth order kernels - are not densities and this assumes that the kernel is a density
In R, for a Gaussian kernel and bandwidth h, with data in x:
I think what you want is:
y <- density(x) x.new <- rnorm(length(x), sample(x, size = length(x), replace = TRUE), y$bw) plot(y) lines(density(x.new), col = "blue")
Note that the density function uses kernel = "gaussian" as default. So to generate gaussian random numbers from a particular density you just need to use rnorm with the mean values equal to the original series and the standard deviation equal to the smoothing bandwidth. In this example I am resampling those mean values to generate different simulations. You can see this example in the density function documentation here.