I'm not entirely sure that even makes sense... for each particular random occurence there's only one interval to which it belongs.... :-|
yes, i completely agree with you there. i didn't say something that goes against that, at least i didn't intend to. you're refering to...:
"avarage number of intervals per random occurance"
...i think. yup, ok i've said it badly. "avarage number of intervals that pass before you get a random occurance". basically, i think, i'm hoping to use m to count intervals rather than events.
you've got e's that occur on avarage say, every 5.5 intervals. with the original function (the way it's used in where i got it from linked to above) the intention behind the function says m is the avarage number of events per interval. that's obviously rediculous with text because you can't have more than one character per interval.
even if it does , these distributions (as I remember) are generally considered memoryless and so you can't work in prior information such as how many characters ago the last e occured etc.
i realise the poisson function in itself, on it's own, won't do that for me, but that additional part you mention is very easy to do with usual c programming around / extra to the poisson function: no problem, honest.
what are you trying to do anyway? text compression?
text analysis, i think it is.
i've posted this question on a maths forum but no-one's answered, but then no-one ever answers me on that particular board! :) but i wrote the question differently there. this is the main chunk from that in case that explains it better than i have already (sorry this is getting *so* long :/ and i honestly have quite a strong suspician the answer may be very simple? i don't know) :
simple, short version:
is it possible, instead of using the equation to give the likelyhood of the number of event occurances in an interval (as it is at the moment), rather the number of intervals that might pass before an event occurance ?
wordy version:
the way the poisson function is used originally, from where i got it from, the variable m (0...19 in the above results) represents: the number of likely occurances of an event in an interval. so 6, represents 6 events occuring in an interval (emphasis: in 1 single interval).
but that doesn't tally up with what i'd like to use it for. here's a description of the situation that i'd like to apply the poisson function to:
1. each interval in space are identicle in size to each other (which is the same as in the original situation).
2. events, if any, fall exactly into intervals - an event can't be half in one interval and half in another (* see note).
3. there can't be more than one event in an interval (different to the original).
(* point 2 maybe irrelevent, or no different from the original in any case. i'm not sure. there's a diagram giving a visual representation of the original being applied on this page with 50 intervals and 50 events: http://info.bio.cmu.edu/courses/03438/pbc97poisson/poissonpage.html but i think possibly the whole of point 2 may be irrelevent but i've included it just to be safe. - probably can completely ignore point 2.)
the main difference between the original situation and the one i'd like to apply the poisson formula to is this: there's absolutely only 2 possible states an interval can be in: no event, or an event.
(btw what i've described there is normal text, and an interval is a character position and an event is a particular pre-chosen character, say an 'e'. so a non event would be any character other than an 'e', the pre-chosen character. and m, the avarage occurance of the chosen character in the text.)
applying the results from the c code above, to the situation i've just described, and say the first interval (interval number 1) contains an event: would it then be ok / correct to say "the likelyhood of an event that occurs on avarage every 5.5 intervals at say, interval number 3, is 11.33%. and the likelyhood of an event being at say, position 11, is 1.43%" ?