Relaxation of monotone coupling conditions: Poisson approximation and beyond

Fraser Daly, Oliver Johnson

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
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It is well-known that assumptions of monotonicity in size-bias couplings may be used to prove simple, yet powerful, Poisson approximation results. Here we show how these assumptions may be relaxed, establishing explicit Poisson approximation bounds (depending on the first two moments only) for random variables which satisfy an approximate version of these monotonicity conditions. These are shown to be effective for models where an underlying random variable of interest is contaminated with noise. We also give explicit Poisson approximation bounds for sums of associated or negatively associated random variables. Applications are given to epidemic models, extremes, and random sampling. Finally, we also show how similar techniques may be used to relax the assumptions needed in a Poincar\'e inequality and in a normal approximation result.
Original languageEnglish
Pages (from-to)742-759
Number of pages18
JournalJournal of Applied Probability
Issue number3
Early online date16 Nov 2018
Publication statusPublished - 2018


  • Monotone coupling
  • (negative) association
  • Poisson approximation
  • Poincare inequality
  • normal approximation
  • size biasing
  • stochastic ordering


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