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Activity Number: 106 - Empirical Transforms, Saddlepoint Approximations, and Risk Assessment with Some Applications
Type: Topic Contributed
Date/Time: Monday, July 31, 2017 : 8:30 AM to 10:20 AM
Sponsor: Section on Risk Analysis
Abstract #322801 View Presentation
Title: On Distributions of Ratios
Author(s): Simon Broda* and Raymond Kan
Companies: University of Amsterdam and University of Toronto
Keywords: Characteristic Function ; Fieller--Creasy Problem ; Inversion Formula ; Saddlepoint Approximation

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 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.

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