On Tuesday 29 June 2004 01:48 pm, Steve S wrote: > Dear All, > > I wonder if there is a probability distribution where you can specify when > a certain event start and finish within a fixed period? For example I might > specify the number of period to be 5, and a random vector from this > distribution might give me: > 0 1 1 1 0 > > where 1 is always adjacent to each other? > > This can never happen: 0 0 1 0 1 for example. > Well, I'll have a go. Let's call it the start-finish distribution. We have a p (period) and d (duration). As there must be an "off" observation (otherwise we don't know the duration), It's fairly easy to enumerate the outcomes for a given period:
d start(s) finish(f) count 1 1:n-1 2:n n-1 2 1:n-2 3:n n-2 ... n-1 1 n-1 1 Assuming that all outcomes are equally likely, the total number of outcomes is: n(n-1)/2 thus the probability of a given d occurring is: P[d|n] = 2(n-d)/n(n-1) The probabilities of s and f over all d are inverse over the values k in 1:n P[s=k|n] = (n-k-1)/(n-1) P[f=k|n] = (k-1)/(n-1) giving, I think, a monotonic function for s and f. > My apology for this strange question! > My apology if this is no use at all. Jim ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
