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The method can also be used to generate random numbers for discrete distributions as well. For example, we can generate random numbers according to a Poisson distribution with a value λ = 5. As you can see in the histogram, we are generating a very similar amount of counts for each possible value that the random variable can take:

rpois_result = data.frame(rpois = rpois(10000,5))
inverse_way = data.frame(inverse = qpois(runif(10000),5))
total_table = cbind(rpois_result,inverse_way)
transp_table = gather(total_table)
colnames(transp_table) = c("method","value")
ggplot(transp_table, aes(x=value,fill=method)) + geom_histogram(alpha=0.8,binwidth=1)

This yields the following overlaid histogram: