On Distributions of Ratios
Copyright policy )On Distributions of Ratios
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.
- THE GOVERNING COUNCIL OF THE UNIVERSITY OF TORONTO Canada
- University of Toronto Canada
- University of Zurich Switzerland
- University of Amsterdam Netherlands
- UNIVERSITEIT VAN AMSTERDAM Netherlands
330, 1101 Agricultural and Biological Sciences (miscellaneous), 10003 Department of Finance, 1100 General Agricultural and Biological Sciences, 510, Simultaneous Equations, Inversion Formula, 2604 Applied Mathematics, 1804 Statistics, Probability and Uncertainty, C15, 2613 Statistics and Probability, 2600 General Mathematics, ddc:330, Saddlepoint Approximation, Weak Instruments, Bootstrap, 620, 330 Economics, C63, C46, Characteristic Function, Instrumental Variables, C26, Characteristic Function, Inversion Formula, Saddlepoint Approximation, Simultaneous Equations, Instrumental Variables, Weak Instruments, Bootstrap, jel: jel:C63, jel: jel:C46, jel: jel:C26, jel: jel:C15
330, 1101 Agricultural and Biological Sciences (miscellaneous), 10003 Department of Finance, 1100 General Agricultural and Biological Sciences, 510, Simultaneous Equations, Inversion Formula, 2604 Applied Mathematics, 1804 Statistics, Probability and Uncertainty, C15, 2613 Statistics and Probability, 2600 General Mathematics, ddc:330, Saddlepoint Approximation, Weak Instruments, Bootstrap, 620, 330 Economics, C63, C46, Characteristic Function, Instrumental Variables, C26, Characteristic Function, Inversion Formula, Saddlepoint Approximation, Simultaneous Equations, Instrumental Variables, Weak Instruments, Bootstrap, jel: jel:C63, jel: jel:C46, jel: jel:C26, jel: jel:C15
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