From: horst.kraemer@snafu.de (Horst Kraemer) Newsgroups: alt.sci.math.probability,alt.sci.math.statistics.prediction,sci.math.num-analysis,sci.stat.math Subject: Re: Scaling of probability curve? Date: Tue, 22 Dec 1998 19:22:56 GMT On 22 Dec 1998 14:31:31 GMT, "Abbot Cooper" wrote: > I have a known historical distribution of patients, expressed as a > probability "curve" of having X number of patients arrive on any given day > to a certain area of the hospital. For instance, the following: > > 0 patients = 25% > 1 patient = 50% > 2 patients = 25% > If you add up the probabilities for each of these (1 * .50) + (2 * .25), > you get an overall average of 1 patient per day. The question that I am > trying to answer is, how can I come up with a new "curve" for a predicted > change in the overall volume. I have done this for some simple examples > such as above, but don't know how to obtain a formula to work in any > instance or for more complex curves. For instance, one of the example I > _can_ do is to double the above curve to the following: A "reasonable probability distribution" for a given average m (of patients per day) of events which are "infrequent" in a certain sense is the POISSON distribution. m^k Pr { n = k } = ---- * exp (-m) k! For m = 1 the probabilities will be 0 0.36788 1 0.36788 2 0.18394 3 0.06131 4 0.01533 5 0.00307 ... m=1.5 0 0.22313 1 0.33470 2 0.25102 3 0.12551 4 0.04707 5 0.01412 ... m=2.0 0 0.13534 1 0.27067 2 0.27067 3 0.18045 4 0.09022 5 0.03609 ... They add up to 1 if you take the limit n->oo. This model fits many phenomena surprisingly well, like the number of telephone calls within a certain period of time, the number of persons arriving at a counter asking for service etc... A famous application of this distribution was a comparision of the number of persons killed by a kick of a horse in a polish cavalry regiment within subsequent years in the beginning of the century. Regards Horst