{"paper":{"title":"Orthonormal polynomial expansions and lognormal sum densities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Patrick J. Laub, Pierre-Olivier Goffard, S{\\o}ren Asmussen","submitted_at":"2016-01-08T03:41:10Z","abstract_excerpt":"Approximations for an unknown density $g$ in terms of a reference density $f_\\nu$ and its associated orthonormal polynomials are discussed. The main application is the approximation of the density $f$ of a sum $S$ of lognormals which may have different variances or be dependent. In this setting, $g$ may be $f$ itself or a transformed density, in particular that of $\\log S$ or an exponentially tilted density. Choices of reference densities $f_\\nu$ that are considered include normal, gamma and lognormal densities. For the lognormal case, the orthonormal polynomials are found in closed form and i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01763","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"}