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On distributions of ratios

Author

Listed:
  • Simon A. Broda
  • Raymond Kan

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.

Suggested Citation

  • Simon A. Broda & Raymond Kan, 2016. "On distributions of ratios," Biometrika, Biometrika Trust, vol. 103(1), pages 205-218.
    • Handle: RePEc:oup:biomet:v:103:y:2016:i:1:p:205-218.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv052
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    Cited by:

    1. Jozef Hanč & Martina Hančová & Dominik Borovský, 2025. "Novel computational approaches for ratio distributions with an application to Hake’s ratio in effect size measurement," Statistical Papers, Springer, vol. 66(5), pages 1-27, August.

    More about this item

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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