Compound Poisson Approximation via Information Functionals

@article{Barbour2010CompoundPA,
  title={Compound Poisson Approximation via Information Functionals},
  author={Andrew D. Barbour and Oliver Johnson and Ioannis Kontoyiannis and Mokshay M. Madiman},
  journal={ArXiv},
  year={2010},
  volume={abs/1004.3692}
}
An information-theoretic development is given for the problem of compound Poisson approximation, which parallels earlier treatments for Gaussian and Poisson approximation. Nonasymptotic bounds are derived for the distance between the distribution of a sum of independent integer-valued random variables and an appropriately chosen compound Poisson law. In the case where all summands have the same conditional distribution given that they are non-zero, a bound on the relative entropy distance… 

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