The Fragile Coupon Collector: Random Deadlines, Critical Fragility, and Optimal Sampling
Year: 2026
Type: article
Abstract: We study coupon collection when each type is at risk of disappearing until its first observation, after which it becomes permanently safe. Sampling follows a fixed independent and identically distributed law. For uniform sampling and common fragility, the success probability is the probability-generating function of a pre-discovery exposure statistic. An independent weighted-geometric decomposition gives an exact product, a critical disappearance scale of n−2, and a central limit theorem with a Berry–Esseen bound. For common fragility 0
Source: Mathematics
DOI: 10.3390/math14203729
Author: Igor Kleiner
Institutions: Holon Institute of Technology, University of Haifa
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7221762224