Author: Andrew Dados
Date: 07:33:20 12/31/01
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On December 31, 2001 at 10:18:11, Robert Pope wrote: >On December 31, 2001 at 09:44:52, Andrew Dados wrote: > >> >>Suppose I am getting tons of scores for some experiment which outcome will obey >>known distribution (In my problem it is Poisson distribution; type of >>distribution should not matter). >> >>I can't store all scores, but I need to know average and mean parameters, so I >>could recreate distribution function at some time later. How can I store some >>set of data as small as possible to be able to add new scores to it and still >>get my mean/sigma right? >> >>Example: One experiment is 1000 tosses of a coin. In this case outcome is number >>of heads. I will collect unspecified number of such results. In this case I >>could simply store an array of 1000 counters, but I can't afford it. Average >>number can be easily stored and incrementally updated with 2 ints: total sum and >>number of experiments. Can some similar trick be done to recalculate mean value >>after new score comes in? >> >>Chess example (closer to my problem): I have a chess position for which I am >>getting time-to-solve results from many players. So their rating distribution is >>'predefined' here. The more samples I will collect, the more accurately I can >>assing a rating for some new player solving this position. I can not collect all >>separate times-to-solve. So for each player I need to update some totals to be >>able to calculate mean from those totals (average is easy). Can this be >>accurately done? >> >>..and no... while it sounds like that - it is not some school assignment. :) >> >>-Andrew- > >I'm not sure about your terminology here. In statistics, mean _is_ the average, >the way most people think about it. Do you intend to say standard deviation? > >The poisson distribution only has one parameter, the mean (sum(Xi)/N). The >standard deviation, sigma, is equal to the mean by definition. It sounds like >you already know how to update this statistic. E.g. If you know the number of >prior observations included in your current sample mean, N, you can update the >sample mean with a new observation like this: newMean = >(oldMean+(X[i+1]/N))*N/(N+1). Or you can keep a running total Sum(X[i]) and a >running total N. Thanks.. and indeed I didn't bother looking up poisson distribution formulas. I've always confused mean with SD in english... However question still stands for other distributions. Can standard deviation be incrementally re-calculated in similar way? Or do I have to approximate it with some 'delta average' tricks, which are way too rough. -Andrew-
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