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The exact distribution function of the ratio of two dependent quadratic forms

Author

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  • Edmund Rudiuk
  • Aleksander Kowalski

Abstract

A closed-form representation of the distribution function of the ratio of two linear combinations of Chi-squared variables is derived. The ratio is of the following form R = (X + aY)/(bY + Z), where X, Y, Z are independent Chi-square variables and a, b > 0. Two methods of obtaining the distribution function of this ratio are used. The exact density function of such a ratio is then obtained by differentiation. Two numerical examples are provided.

Suggested Citation

  • Edmund Rudiuk & Aleksander Kowalski, 2018. "The exact distribution function of the ratio of two dependent quadratic forms," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(21), pages 5227-5240, November.
    • Handle: RePEc:taf:lstaxx:v:47:y:2018:i:21:p:5227-5240
    DOI: 10.1080/03610926.2017.1388400
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