Normalizing data for Poisson MLE [closed]

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I am trying to find the lambda parameter for a dataset by MLE. This seems rather easy as described here http://en.wikipedia.org/wiki/Poisson_distribution

My problem is that I am trying to fit data that does not correspond easily with the low values of k employed by those examples. Specifically, my data is a distribution of cost estimates for a project (usually in the thousands) that I would like to fit to a poisson distribution.

Question: How do I "normalize" or "scale" my data so I can estimate the Lambda parameter, which I would expect to be somewhere around 3-5?

I hope I am not completely off with this question, should be possible, shouldn't it?

Thanks for your comments.

Answer 1

Since you only have one parameter to fit, I suggest calculating the Likelihood over a grid of lambda parameters, and looking at the graph of Likelihood versus Lambda by e.g. importing the results into Excel or Matlab. If it's fast to calculate one Likelihood, you could have 1000 values easily, e.g. from lambda = 0.01 to lambda = 10 with a stepsize of 0.01. Looking at the graph, you can then work out the maximum by inspection. If there's something strange (e.g. the data doesn't fit Poisson very well at all), then you'll something unusual in that graph and you'll then need to decide on next steps.