The exact distribution function of the ratio of two dependent quadratic forms |
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| Authors: | Edmund Rudiuk Aleksander Kowalski |
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| Institution: | 1. Mathematics, Physics and Geology Department, Cape Breton University, Sydney, Nova Scotia, Canadaedmund_rudiuk@cbu.ca;3. Institute of Mathematics, Maria Curie-Sklodowska University, Lublin, Poland |
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| 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. |
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| Keywords: | Distribution function Gamma and chi square variables Linear combination Quadratic forms |
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