On statistical characteristics of the product of two correlated chi-square variables

The distribution of the product of two variables is important in portfolio diversification model and in economic forecasting. We derive the distribution of the product of two chi-square variables when they are correlated through a bivariate chi-square distribution. Closed form expressions for raw moments, centered moments, coefficient of skewness and kurtosis are obtained. The density function is also graphed. The results match with the distribution of the product of two independent chi-square variables in case the coefficient correlation in our model vanishes. They are often extended to sample variances of bivariate normal distribution.