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distributionpoisson

PoissonDistribution determinate lambda


If I have an event like this:

"In mean I create 5 object every ten minute". I have to use the Poisson Distribution

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

I must determinate the parameter lambda. I think lambda is (temporalInterval / mean) that in this case is (10/5). is it correct? I don't know if this solution is correct. Anyone can help me?


Solution

  • Lambda is the rate of the observed process. Rates are of the form "count per unit". If your Poisson is being used to describe a temporal process, the rate is E[count / unit time] and an unbiased estimate of it is observed count / observed time. If you have observed 5 objects in 10 minutes, the estimated rate is 0.5 per minute. Poisson rates can be scaled to different time units if desired, so a rate of 0.5 per minute is also 5 per 10 minutes or 30 per hour. The choice of a useful unit of time is up to you, but make sure you use units consistently throughout a problem.

    Lambda is not a probability, as stated by another respondent. That claim is trivially disproven since lambda can be any positive value, while probabilities must be numbers between zero and one.