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log likelihood output from the distribution fitter app

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William Krauter
William Krauter on 7 Jul 2020
Answered: Jeff Miller on 7 Jul 2020
I have used the Distribution Fitter app to fit Weibull and Rayleigh distribution to a histogram.
When I make the Weibull fit, I get a Log likelihood value of -1.26131e+06.
When I make the Rayleigh fit, I get a Log likelihood value of -1.26173e+06.
I would venture to guess these Log likelihood values come from a min\max calculation. Consequently, these values are the highest\lowest points on the curve.
I want to say the Rayleigh fit is better since it is the smallest.

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Answers (1)

Jeff Miller
Jeff Miller on 7 Jul 2020
Just be a bit careful here...
  1. I think those log likelihood values are likelihoods under the maximum likelihood parameter estimates for each distribution. In that case, larger is better, so the data have a higher likelihood under the Weibull than the Rayleigh. I don't know about the Dist Fitter, but the usual parameter search routines minimize the negative of the log likelihood, and you can also see that the negative of the Weibull value is smaller than the minimum of the Rayleigh value.
  2. Just because distribution A fits your particular data set better than distribution B, it does not follow that distribution A is the right one and distribution B is the wrong one. Due to random variability, data from distribution B might look like they come from A, or vice versa. To get some sense of this kind of variability, you can do some simple simulations. Generate 1000 datasets from A (with the number of observations you have), fit both A and B to each one, and see how often A fits better than B. Then generate from B.
HTH

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