On Some Characteristics of the Joint Distribution of Sample Variances

Abstract

The joint distribution of correlated sample variances and their product moments have been derived. Finite expressions have been derived for product moments of sample variances of integer orders. Marginal and conditional distributions, conditional moments, coefficient of skewness and kurtosis of conditional distribution of a sample variance given the other variance have also been discussed. Shannon entropy of the distribution is also derived. When the variables are uncorrelated, the resulting characteristics match with the independent case of sample variances.