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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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Joarder, A.H. Moments of the product and ratio of two correlated chi-square variables. Stat Papers 50, 581–592 (2009). https://doi.org/10.1007/s00362-007-0105-0
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DOI: https://doi.org/10.1007/s00362-007-0105-0
Keywords
- Bivariate chi-square distribution
- Moments
- Product of correlated chi-square variables
- Ratio of correlated chi-square variables