This family of functions computes univariate descriptive statistics for the products of two variables denoted as "x" and "y" (e.g., mean(x * y) or var(x * y)) and the covariance between the products of "x" and "y" and of "u" and "v" (e.g., cov(x * y, u * v) or cor(x * y, u * v)). These functions presume all variables are random normal variables.

Available functions include:

estimate_mean_prod Estimate the mean of the product of two variables: x * y.

estimate_var_prod Estimate the variance of the product of two variables: x * y.

estimate_cov_prods Estimate the covariance between the products of two pairs of variables: x * y and u * v.

estimate_cor_prods Estimate the correlation between the products of two pairs of variables: x * y and u * v.

`estimate_mean_prod(mu_x, mu_y, cov_xy)`estimate_var_prod(mu_x, mu_y, var_x, var_y, cov_xy)

estimate_cov_prods(mu_x, mu_y, mu_u, mu_v, cov_xu, cov_xv, cov_yu, cov_yv)

estimate_cor_prods(mu_x, mu_y, mu_u, mu_v, var_x, var_y, var_u, var_v,
cov_xu, cov_xv, cov_yu, cov_yv, cov_xy, cov_uv)

mu_x

Expected value of variable x.

mu_y

Expected value of variable y.

cov_xy

Covariance between x and y.

var_x

Variance of variable x.

var_y

Variance of variable y.

mu_u

Expected value of variable u.

mu_v

Expected value of variable v.

cov_xu

Covariance between x and u.

cov_xv

Covariance between x and v.

cov_yu

Covariance between y and u.

cov_yv

Covariance between y and v.

var_u

Variance of variable u.

var_v

Variance of variable v.

cov_uv

Covariance between u and v.

An estimated statistic computed from the products of random, normal variables.

Bohrnstedt, G. W., & Goldberger, A. S. (1969). On the exact covariance of products of random variables.
*Journal of the American Statistical Association, 64*(328), 1439. https://doi.org/10.2307/2286081

Goodman, L. A. (1960). On the exact variance of products.
*Journal of the American Statistical Association, 55*(292), 708. https://doi.org/10.2307/2281592