#5739. Efficient importance sampling for large sums of independent and identically distributed random variables

August 2026publication date
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Journal’s subject area:
Statistics and Probability;
Statistics, Probability and Uncertainty;
Computational Theory and Mathematics;
Theoretical Computer Science;
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Abstract:
We discuss estimating the probability that the sum of nonnegative independent and identically distributed random variables falls below a given threshold, i.e., P(?i=1NXi??), via importance sampling (IS). We are particularly interested in the rare event regime when N is large and/or ? is small. The exponential twisting is a popular technique for similar problems that, in most cases, compares favorably to other estimators. However, it has some limitations: (i) It assumes the knowledge of the moment-generating function of Xi and (ii) sampling under the new IS PDF is not straightforward and might be expensive. The aim of this work is to propose an alternative IS PDF that approximately yields, for certain classes of distributions and in the rare event regime, at least the same performance as the exponential twisting technique and, at the same time, does not introduce serious limitations.
Keywords:
Exponential twisting; Gamma IS PDF; Importance sampling; Rare event

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