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

Edmund Rudiuk and Aleksander Kowalski

Communications in Statistics - Theory and Methods, 2018, vol. 47, issue 21, 5227-5240

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.

Date: 2018
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DOI: 10.1080/03610926.2017.1388400

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