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I have a number of historical observations, let's say they represent the number of car accidents per day for a certain region. I don't know what the true distribution or probability is, but want to work out the best estimate of the probability of today's number of car accidents being higher than a certain number and also the distribution for this probability. How do I go about doing this?

SoftMemes
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You would use the Poisson Distribution

http://en.wikipedia.org/wiki/Poisson_distribution

and if you have the time period use the Homogenous Poisson process

http://en.wikipedia.org/wiki/Poisson_process#Homogeneous

ccsv
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  • That a good starting point, but do investigate with your data if a Poisson distribution is a good fit: https://stats.stackexchange.com/questions/80043/fitting-data-to-a-poisson-distribution-what-are-the-errors and then https://stats.stackexchange.com/questions/286003/what-to-do-when-count-data-does-not-fit-a-poisson-distribution – kjetil b halvorsen Feb 19 '22 at 01:25