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.
For illustrative purposes, we adopt the parametric bootstrapping proposed by Henze (1996) to calculate the critical numbers or thresholds of the KS test
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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.