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For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of $X_{k:n}$. For an extreme $X_{k:n}$, the asymptotic independence property of spacings fails for $F$ in the domain of attraction of Fr\\'{e}chet and Weibull ($\\alpha \\neq 1$) di"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1702.05910","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2017-02-20T09:51:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"9349196b8fa5295bc5c5e71fe37197b5418ded11fcfa19a65c5566587f28d317","abstract_canon_sha256":"cf0c9a92a02b3d7711b80d12265c3c82345ad93c807a7e2b9a2d34131d938046"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:24.914061Z","signature_b64":"NPMm/L9K4CX5U9Yry0WPTc2xEq3WVSW4wjCyzCuiB8t0YNEiXsis4hHYmvbS5harsLTq47+R4Apa/oXxOSHZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b75ef1afa04bcdb082e55855e7229caee9cc636585c1fcce70e6b14c1a8e02c8","last_reissued_at":"2026-05-18T00:50:24.913303Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:24.913303Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spacings Around An Order Statistic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Fangyuan Zhang, H. 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