The exact distribution function of the ratio of two dependent quadratic forms. Issue 21 (2nd November 2018) - Rudiuk, Edmund; Kowalski, Aleksander
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.