Dear list members, I have a series of /unequal/ probabilities [p1,p2,...,pk], describing mutually exclusive events, and a "remainder" class with a probability p0=1-p1-p2-....-pk, and need to calculate, for a given number of trials t>=k, the combined probability that each of the classes 1...k contains at least 1 "event" (the remainder class may be empty).
To me this reaks of a sum of multinomial distributions, and indeed, I can readily calculate the correct answer for small figures t,k using a small R program. However, in my typical experiment, k ranges from ~20-60 and t from ~40-100, and having to calculate these for about 6e9 experiments, a quick calculation on the back of a napkin shows me that I will not be able to complete these calculations before the expected end of the universe. I already figured out that in this particular case I may use reciprocal probabilities, and if I do this I get an equation with "only" 2^k terms, which would shorten my computations to a few decades. Isn't there a faster (numerical approximation?) way to do this? R has dbinom /and/ pbinom functions, but unfortunately only a dmultinom and no pmultinom function... perhaps because there is no (known) faster way? with kind regards, Theo Borm ______________________________________________ [email protected] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
