Efficient importance sampling for large sums of independent and identically distributed random variables

@article{Rached2021EfficientIS,
  title={Efficient importance sampling for large sums of independent and identically distributed random variables},
  author={Nadhir Ben Rached and Abdul-Lateef Haji-Ali and Gerardo Rubino and Ra{\'u}l Tempone},
  journal={Stat. Comput.},
  year={2021},
  volume={31},
  pages={79}
}
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., $$\mathbb {P}(\sum _{i=1}^{N}{X_i} \le \gamma )$$ P ( ∑ i = 1 N X i ≤ γ ) , via importance sampling (IS). We are particularly interested in the rare event regime when N is large and/or $$\gamma $$ γ is small. The exponential twisting is a popular technique for similar problems that, in most cases, compares… 

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