Stein's method for comparison of univariate distributions

@article{Ley2014SteinsMF,
  title={Stein's method for comparison of univariate distributions},
  author={Christophe Ley and Gesine Reinert and Yvik Swan},
  journal={arXiv: Probability},
  year={2014}
}
We propose a new general version of Stein's method for univariate distributions. In particular we propose a canonical definition of the Stein operator of a probability distribution {which is based on a linear difference or differential-type operator}. The resulting Stein identity highlights the unifying theme behind the literature on Stein's method (both for continuous and discrete distributions). Viewing the Stein operator as an operator acting on pairs of functions, we provide an extensive… 

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