{"paper":{"title":"Properties and Applications of some Distributions derived from Frullani's integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Rose Baker","submitted_at":"2014-08-15T08:03:36Z","abstract_excerpt":"Frullani's integral dates from 1821, but a probabilistic interpretation of it has never been made. In this paper, Frullani's integral formula is shown to result from mixing a lifetime distribution by allowing the logarithm of the scale factor to be uniformly distributed over a finite range. This gives a class of long-tailed distributions related to slash distributions, where the pdf is simply expressed in terms of the survival function of the `parent' distribution. The resulting survival distributions have all moments finite, and can exhibit the bimodal hazard functions sometimes seen in pract"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.3490","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"}