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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?

marc_s
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doflamingo
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2 Answers2

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Lambda in the Poisson distribution is the expected number of times that an event occurs. For example, say you were observing shoppers entering a store over 10 minute intervals throughout 1 day and saw had the following frequencies:

  • 0 Entrances Observed 20 times
  • 1 Entrances Observed 50 times
  • 2 Entrances Observed 30 times
  • 3 Entrances Observed 28 times
  • 4 Entrances Observed 12 times
  • 5 Entrances Observed 4 times

Altogether 262 people entered the store: [20 * (0) + 50 * (1) + 30 * (2) + 28 * (3) + 12 * (4) + 5 * (4)]
Over 144 time periods [20 + 50 + 30 + 28 + 12 + 4]
So lambda is the average number of entries per time period. 262/144 = 1.8194...

Poisson says p(x, lambda) = [e^(-lambda) * (lambda)^x] / x!

So the probability of 0 people entering the store would be estimated as: p(0, 1.819) = [e^(-1.819) * (1.819)^0] / 0! = [0.162 * 1] / 1 = 0.162

We actually saw 0 people come in 20 times in 144 checks so the observed chance of 0 people entering was 20/144 = 0.138. Pretty close!

So basically you are saying you have 5 occurrences every 10 minutes so for you lambda would be 5. The average number of occurrences in a 10 minute window.

Hope this helps.

Brett
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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.

pjs
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