On distributions of ratios

Simon Broda and Raymond Kan

Biometrika, 2016, vol. 103, issue 1, 205-218

Abstract: 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.

Date: 2016
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Working Paper: On Distributions of Ratios (2013)
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