[This article was first published on Why? » R, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

As I mentioned in a recent post, I’ve just received a copy of Advanced Markov Chain Monte Carlo Methods. Chapter 1.4 in the book (very quickly) covers random variable generation.

## Inverse CDF Method

A standard algorithm for generating random numbers is the inverse cdf method. The continuous version of the algorithm is as follows:

1. Generate a uniform random variable $U$

2. Compute and return $X = F^{-1}(U)$

where $F^{-1}(cdot)$ is the inverse of the CDF. Well known examples of this method are the exponential distribution and the Box-Muller transform.

## Example: Logistic distribution

I teach this algorithm in one of my classes and I’m always on the look-out for new examples. Something that escaped my notice is that it is easy to generate RN’s using this technique from the Logistic distribution. This distribution has CDF

$displaystyle F(x; mu, s) = frac{1}{1 + exp(-(x-mu)/s)}$
and so we can generate a random number from the logistic distribution using the following formula:
$displaystyle X = mu + s logleft(frac{U}{1-U}right)$

Which is easily converted to R code:
 myRLogistic = function(mu, s){   u = runif(1)   return(mu + s log(u/(1-u))) }

To leave a comment for the author, please follow the link and comment on their blog: Why? » R.

R-bloggers.com offers daily e-mail updates about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.
Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

# Never miss an update! Subscribe to R-bloggers to receive e-mails with the latest R posts.(You will not see this message again.)

Click here to close (This popup will not appear again)