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We have a look at the behaviour of stop-loss transforms when the order goes to infinity. Explicit identification of the limit is obtained when the random variable is gamma or Weibull distributed, highlighting that very different limiting behaviour may happen.

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This page is a summary of: On the behavior of the high order stop-loss transform for convolutions with some applications, Communication in Statistics- Theory and Methods, September 2020, Taylor & Francis,
DOI: 10.1080/03610926.2020.1818101.
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