{"paper":{"title":"Fragility Distributions and their approximations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Xia, H.L. Gan","submitted_at":"2014-02-05T05:09:38Z","abstract_excerpt":"Given a sequence of $n$ identically distributed random variables with common distribution $F$, the \\emph{fragility distribution of order $m$}, represented by $\\FD$, is the limit conditional distribution of the number of exceedances given there are at least $m$ exceedances, as the threshold tends to the right end point of $F$. In this paper we are concerned with the existence of $\\FD$ and its asymptotic behaviour when $n$ becomes large. For a stationary sequence with its exceedance process converging to a compound Poisson process, we derive an explicit formula for calculating $\\lim_{n \\to \\inft"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0934","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}