[R] faster computation of cumulative multinomial distribution

[theo borm]

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....

http://www.top500.org/list/2006/11/100

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

Cheers,

Theo