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Q: Function for calculating approx. Poisson distribution probabilities? ( Answered ,   0 Comments )
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 Subject: Function for calculating approx. Poisson distribution probabilities? Category: Science > Math Asked by: donkan-ga List Price: \$2.00 Posted: 06 Dec 2002 17:55 PST Expires: 05 Jan 2003 17:55 PST Question ID: 120632
 `Please break this down for a non-statistition.` Request for Question Clarification by mathtalk-ga on 06 Dec 2002 18:13 PST ```Hi, donkan-ga: Please clarify what you mean by "calculating" approximate Poisson distribution probabilities. Are you looking for something you can do in your head? on the back of an envelope? with a TI calculator in hand? Or were you asking about numerical methods for approximating the Poisson distributions to any desired degree of accuracy? For a well-targeted answer, perhaps you could also amplify on the non-statistician situation. What are your skills and interests in relation to this exercise? For example, you might be building an Excel spreadsheet to predict light bulb lifetimes; you know Excel but not the statistical application. regards, mathtalk-ga``` Clarification of Question by donkan-ga on 07 Dec 2002 03:06 PST ```mathtalk-ga, sorry for the lack of precision in my question. I just remember years ago putting such a function in a calculator something like a TI that could answer questions such as this, which I just made up: "Assume that fatal accidents at a busy intersection A are randomly distributed in time, and an average of 3/year occur. What is the probability that exactly 5 will occur at A in 2003?" After seeing your request for clarification I found The Poisson Pit (http://www.anesi.com/poisson.htm), but I'm not sure I understand their example. I think their p(x;m) is what I'm after (and it's degree of accuracy). If I use their p(x;m) function for my example, I think I'd use m=3, but what is my x? I first came across the Poisson Distribution many years ago in a freshman physics class. We were given Geiger counters and asked to describe the distribution of "cosmic rays/particles" hitting the counter. The answer I believe was the PD. So let's use this as another example. Let's say that an average of 3 particles hit the counter every 10 minutes. How do I get the probability of exactly 30 hits in the next hour? What are the x and m? I hope this narrows down my question. Forget the non-statistician part. I'm not one, obviously, but I think I'll be able to follow your answer as it pertains to p(x;m).```
 ```Hi Donkan-ga, First, to answer your specific questions: in your first example with car accidents, you would indeed take m=3, which is the expected number of fatal accidents in a year. As for x, you would set x=5 to get the probability p(x;m) of exactly 5 fatal accidents occurring in a given year in that intersection. In the second example, m will be equal to 18, since if the expected number of particle hits every 10 minutes is 3, then in one hour it will be 3*6=18. x would be 30, since you are interested in the probability of getting exactly 30 hits. Now, for a more general explanation: The Poisson distribution describes the number of "rare events" happening in a given time/space interval. As you seem to already understand pretty well, the type of "rare events" can be anything from car accidents, radioactive particle disintegration, to rain drops hitting a sidewalk or spelling mistakes in a newspaper page. The function p(x;m) gives the probability that exactly x events will happen, provided that m is the expected number of events happening. It is given by the expression p(x;m) = e^(-m) m^x / x! ("^" means "to the power of", "!" means factorial) (x = 0,1,2,3, ...) Sometimes you know the "m" for a different time or space interval than that for which you want to compute probabilities. For instance, if I know that an average page of a certain newspaper contains 5 spelling mistakes, then the probability that on a given day there will be 7 mistakes on the first two pages will be p(7;10) - I take m=5*2 to account for the number of pages I look at. Further information: Poisson Distribution - from Eric Weisstein's world of Mathematics http://mathworld.wolfram.com/PoissonDistribution.html Hope this helps, dannidin```
 donkan-ga rated this answer: and gave an additional tip of: \$2.00 `Outstanding answer. Thank you!`