Thursday, February 4, 2010

A Problem with the Poisson Distribution.

The λ in the Poisson distribution is the probability that a single event will be observed in a given time interval. Its values range from 0 to 1. In the earthquake fits the values of λ were 151.227 for the global earthquakes and 43.412 for the California earthquakes which fall outside the 0 to 1 range. One can't simply rescale the magnitudes to reduce the λs. A normal distribution is similar in form but more scalable. Replacing λ with r Δt or r ΔM would give a larger value but that runs contrary to the assumption that the probability is a small value so the results are still doubtful.

Conclusion: Poisson = FAIL

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