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.
Then according to (10), GN B(ν,p)(ν) =EΨ(ν+Y 1)−Ψ(ν)−log 1 + µ ν = Ψ(ν)−log(p)−Ψ(ν)−log 1 + 1−p p = 0, S5 whereµ=ν(1−p)/pfor NB(ν, p)
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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.