## Monday, December 31, 2012

### On Random Numbers

These days, we take it for granted that it's very simple, and relatively costless, to generate random numbers. Really, these are "pseudo-random numbers", and we should pay careful attention to the quality of the algorithms that are used to generate them, as I've noted previously (and also here) on this blog.

Putting these qualification to one side, however, we've certainly come a long way from having to rely on that famous tome, A Million Random Digits With 100,000 Normal Deviates. Published by the Rand Corporation in 1955, this classic provided (lots of!) random digits that could be used as an aid to simple random sampling, as well random deviates generated from the standard normal distribution. The latter could be used in Monte Carlo simulations, for example.

The following is an extract from a handout that I use in my introductory statistical inference course:

"You’ll no doubt be delighted to learn that the book, A Million Random Digits With 100,000 Normal Deviates, is available on Amazon.com. As is generally the case with their listed books, Amazon has published numerous reviews by past readers of this book. In this particular case, there are reviews from people who seem to have a decent sense of humour.

For example:

• 'Such a terrific reference work! But with so many terrific random digits, it's a shame they didn't sort them, to make it easier to find the one you're looking for.'
• 'Does anybody know about a German translation of this book? I really would be glad, if I can get it in German.'
• 'Wow! The 1,000,000 random digits produced by the Rand Corporation are some of the best random digits out there! I was amazed at some of their selections.'
• 'To whom do I write to report typographical errors? I noticed that the first "7" on the third line page 48 should be a "3". The "7" that's printed there now isn't random. Other than that, this is really an excellent book.'
• 'Critics and audiences are hailing the restoration of this now cult-classic. The stream of consciousness writing style that Dr. Rand pioneered in this daring work was soon picked up by Jack Kerouac and other writers of the beat generation. One can't help but visualize the thick haze of cigarette smoke and booze as Rand would read aloud his digits to a mesmerizing bongo drum beat…………'
• 'Have you Random Digits fans heard the great news? It looks like Universal has picked up the rights to the book and they've already begun production on the film adaptation!'
• 'The rumor mill suggests that Brad Pitt is going to star as, you guessed it, 27473, and Maggie Gyllenhaal is lined up to play 70690. Other stars that are signed include Heath Ledger as the diabolical 91437 and there are some rumors that Robert DeNiro will put in a brief cameo as 22941. The project is going to be directed by Quinten Tarantino, which is why production of his next movie, Grind House, suddenly stopped early this summer. He was obviously focusing on adapting Random Digits for the big screen.'
• 'Expect this one to be the biggest hit of 2007. Forget Spiderman 3, that only contains one digit that was deliberately picked. A Million Random Digits with 100,000 Normal Deviates will kill it at the box office.' "
My handout does actually include some useful information (I hope)!

© 2012, David E. Giles