[R] faster computation of cumulative multinomial distribution

theo borm theo_rstt at borm.org
Mon Apr 2 10:52:33 CEST 2007

Alberto Vieira Ferreira Monteiro wrote:
> Theo Borm wrote:
>>Think of a sort of "power roulette", played with 58 balls
>>simultaneously, with a wheel containing 36 red/black slots of unequal
>>size, and 1 green slot. I need to calculate the probability that each of
>>the 36 red/black slots contains at least one ball.
> Ah, now we come to a more precise problem :-)
>>I have a hunch that it won't work as my p vector typically contains
>>values like:
>>p<-c(0.99, 0.005, 0.003, 0.001, 0.0005, 0.0003, 0.0001, 0.00005,
>>0.00003, 0.00002).
> So you should expect that only 1/50000 will be in the low-prob
> hole in the average?

Or less. And normally I'll have 30-60 holes, with the "remainder" hole 
containing > 98% of the events.

> Hmmm.... That's right. No way to do a Monte Carlo here!

Yes. Its back to square one for me. Maybe I should get a bigger 
computer. I heard that IBM is selling some quite fancy stuff....


Would probably be quite a challenge to coerce R to run on such a machine 



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