On distributions of ratios

• 成果类型: Article
• 署名作者: Broda, Simon A.; Kan, Raymond
• 署名单位: University of Amsterdam; University of Toronto
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asv052
• 发表日期: 2016
• 页码: 205218
• 关键词: generalized confidence-intervals; 2 normal-populations; saddlepoint approximations; resampling methods; bootstrap

摘要

Inversion formulae are derived that express the density and distribution function of a ratio of random variables in terms of the joint characteristic function of the numerator and denominator. The resulting expressions are amenable to numerical evaluation and lead to simple asymptotic expansions. The expansions reduce to known results when the denominator is almost surely positive. Their accuracy is demonstrated with numerical examples.