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It is well known that $W^*$ and $W$ are equal in distribution if and only if $W$ has the generalized Dickman distribution ${\\cal D}_\\theta$. We demonstrate that the Wasserstein distance $d_1$ between $W$, a non-negative random variable with finite mean, and $D_\\theta$ havin"},"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":"1703.00505","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-03-01T21:06:08Z","cross_cats_sorted":["math.NA"],"title_canon_sha256":"12f20db55c97a652d1c34100c5cf28a83b2c2a897740ae03bf1bf46247d315e4","abstract_canon_sha256":"e822b50aa70d1e1a23aab87eb7008411736c49ecf4d7c0e1f11cd0aa447fb6e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:50.031986Z","signature_b64":"7/VzxeHqMz6kD4+Mj0CGZOb9k75jNOPLxC62zC93IqS5wzKqs0HDHZ9g4shdxAO6g235ck/pNvkTP5Ptcf0yAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9c9f9ef3d50ec6443604c2d1d7fd809a5f95f79c40b48e271dd1249e07a9798b","last_reissued_at":"2026-05-18T00:02:50.031291Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:50.031291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non asymptotic distributional bounds for the Dickman Approximation of the running time of the Quickselect algorithm","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA"],"primary_cat":"math.PR","authors_text":"Larry Goldstein","submitted_at":"2017-03-01T21:06:08Z","abstract_excerpt":"Given a non-negative random variable $W$ and $\\theta>0$, let the generalized Dickman transformation map the distribution of $W$ to that of $$ W^*=_d U^{1/\\theta}(W+1), $$ where $U \\sim {\\cal U}[0,1]$, a uniformly distributed variable on the unit interval, independent of $W$, and where $=_d$ denotes equality in distribution. It is well known that $W^*$ and $W$ are equal in distribution if and only if $W$ has the generalized Dickman distribution ${\\cal D}_\\theta$. 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