Please use this identifier to cite or link to this item: `https://hdl.handle.net/10356/178833`
DC FieldValueLanguage
dc.contributor.authorAu, Siu-Kuien_US
dc.date.accessioned2024-07-11T00:52:03Z-
dc.date.available2024-07-11T00:52:03Z-
dc.date.issued2024-
dc.identifier.citationAu, S. (2024). A limit formula and a series expansion for the bivariate Normal tail probability. Statistics and Computing, 34, 152-. https://dx.doi.org/10.1007/s11222-024-10466-wen_US
dc.identifier.issn0960-3174en_US
dc.identifier.urihttps://hdl.handle.net/10356/178833-
dc.description.abstractThis work presents a limit formula for the bivariate Normal tail probability. It only requires the larger threshold to grow indefinitely, but otherwise has no restrictions on how the thresholds grow. The correlation parameter can change and possibly depend on the thresholds. The formula is applicable regardless of Salvage’s condition. Asymptotically, it reduces to Ruben’s formula and Hashorva’s formula under the corresponding conditions, and therefore can be considered a generalisation. Under a mild condition, it satisfies Plackett’s identity on the derivative with respect to the correlation parameter. Motivated by the limit formula, a series expansion is also obtained for the exact tail probability using derivatives of the univariate Mill’s ratio. Under similar conditions for the limit formula, the series converges and its truncated approximation has a small remainder term for large thresholds. To take advantage of this, a simple procedure is developed for the general case by remapping the parameters so that they satisfy the conditions. Examples are presented to illustrate the theoretical findings.en_US
dc.language.isoenen_US
dc.relationRG68/22en_US
dc.relation.ispartofStatistics and Computingen_US
dc.subjectMathematical Sciencesen_US
dc.titleA limit formula and a series expansion for the bivariate Normal tail probabilityen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Civil and Environmental Engineeringen_US
dc.identifier.doi10.1007/s11222-024-10466-w-
dc.description.versionSubmitted/Accepted versionen_US
dc.identifier.volume34en_US
dc.identifier.spage152en_US
dc.subject.keywordsBivariate normal probabilityen_US
dc.subject.keywordsHashorva’s formulaen_US
dc.subject.keywordsPlackett’s identityen_US
dc.subject.keywordsRuben’s formulaen_US
dc.subject.keywordsSalvage’s conditionen_US
dc.description.acknowledgementThe research presented in this paper is supported by Academic Research Fund Tier 1 (RG68/22) from the Ministry of Education, Singapore.en_US
item.grantfulltextembargo_20250801-
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