Non-Uniform Random Variate Generation
Looking for a rigorous mathematical text on efficient random number generation for various statistical distributions? Perhaps you need data generation for simulations or Monte Carlo trials? Then take a look at Non-Uniform Random Variate Generation by Luc Devroye -- it looks to be one of the best collections of its kind.
The text is about one small field on the crossroads of statistics, operations research and computer science. Statisticians need random number generators to test and compare estimators before using them in real life. In operations research, random numbers are a key component In large scale simulations. Computer scientists need randomness In program testing, game playing and comparisons of algorithms.
The book seems geared for these uses:
you are writing a library of random number generators
you want to be confident that you aren't fouling up random number generation (RNG)
you care about performance
you are looking to verify that a software library has done its homework when it comes to RNG implementation details
I've seen citations among R library implementers to Devroye's work; I suspect that other libraries like Apache Commons Math (Java) and NumPy/SciPy do too.
Note: The PDFs are sharp and readable but have some strange encoding issues when it comes to copying, pasting, and searching.
As a side note, the author doesn't hold anything back in explaining why the book is free:
Furthermore, I give anyone the permission, even without asking me, to take these PDF files to a printer, print as many copies as you like, and sell them for profit. If you would like me to advertise the sales points of the hard copies, please let me know. To the libraries: Please do not charge patrons for copying this book. I grant everyone the right to copy at will, for free.
So, there you have it. Eventually, I will do this with all my books. While I love Springer, my honeymoon with them is over. I will of course never start any affairs with the champion bloodsuckers like Elsevier, Kluwer or Dekker. Outfits I like are SIAM (nonprofit), Dover (great pricing) and Oxford University Press (allowing authors to post books on the web). With the arrival of Amazon, book advertising is no longer necessary, and one can publish with any company, really. So, it will be a matter of a few years before the old publishers will come back to the academics on their hands and knees asking for manuscripts. Too late.
I stumbled across this because I am writing a quick simulation to estimate various performance measures in a distributed system, which led me to look around to see what is available. This led me to an online slide deck called A Brief History of Simulation Revisited which referred to Devroye's book.