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 ∞X y=M+1 yfy n = ∞X y=M+1 #{1≤i≤n|Y i =y} ·y n = 1 n nX i=1 Yi1{Yi>M} − →E(Y 11{Y1>M}) almost surely, asn→ ∞
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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.