The median of a jittered Poisson distribution
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Let N_λ and U be two independent random variables respectively distributed as a Poisson distribution with parameter λ >0 and a uniform distribution on (0,1). This paper establishes that the median, say M, of N_λ+U is close to λ +1/3 and more precisely that M-λ-1/3=o(λ^-1) as λ→∞. This result is used to construt a very simple robust estimator of λ which is consistent and asymptotically normal. Compared to known robust estimates, this one can still be used with large datasets (n≃ 10^9).
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