Statistics question on Poisson distribution?

Asked by LostInParadise (32183

) February 25th, 2011

I understand how Poisson distribution can be used to model infrequent events. Let me give a concrete example of the type of calculation I would like to perform.

Suppose we know the rate at which particles arrive at a specified location and suppose the rate is small. We define a collision to be the arrival of two or more particles at the location within the same minute. We can use the Poisson distribution to calculate the probability of a collision during a specified minute. How can you determine the probability of at least one collision during a particular 24 hour period. I do not want to break the day up into one minute intervals. I want to use a continuous time distribution.

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1 Answer

It’s been a while, but I recall the Poisson distribution as being more useful in queuing theory. I also recall that it’s more useful when you are talking about discrete, rather than continuous intervals. Had you asked this 30 years ago, I might have been able to give you a better answer. However, here’s Mathworld’s page on the subject.

IchtheosaurusRex (8681

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