New MLE algorithm and extended negative binomial parameterization that includes Poisson as a limit case, with proof that Poisson data yields consistent recovery of the true Poisson parameters.
In this case,µ=ν(1−p)/pbuilds up a one-to-one correspondence from{(ν, p)|ν∈ (0, νmax], p∈(0,1)}to{(ν, µ)|ν∈(0, ν max], µ∈(0,∞)}, which will pass along the S9 uniqueness of MLE
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From Poisson Observations to Fitted Negative Binomial Distribution
New MLE algorithm and extended negative binomial parameterization that includes Poisson as a limit case, with proof that Poisson data yields consistent recovery of the true Poisson parameters.