# 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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