Moments of the product and ratio of two correlated chi-square variables
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Abstract
The exact probability density function of a bivariate chi-square distribution with two correlated components is derived. Some moments of the product and ratio of two correlated chi-square random variables have been derived. The ratio of the two correlated chi-square variables is used to compare variability. One such application is referred to. Another application is pinpointed in connection with the distribution of correlation coefficient based on a bivariate t distribution.
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Joarder, A. H. (2009). Moments of the product and ratio of two correlated chi-square variables. Stat Papers, 50, 581–592. https://doi.org/10.1007/s00362-007-0105-0