Entropy and the ‘compound’ Law of Small Numbers
نویسندگان
چکیده
An information-theoretic foundation for compound Poisson approximation limit theorems is presented, in analogy to the corresponding developments for the central limit theorem and for simple Poisson approximation. It is shown that the compound Poisson distributions satisfy a natural maximum entropy property within a natural class of distributions. Simple compound Poisson approximation bounds are derived in terms of relative entropy. Finer (near-optimal) approximation bounds are established, using discrete versions of the Fisher information functional.
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