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
)
An estimated statistic computed from the products of random, normal variables.
Expected value of variable x.
Expected value of variable y.
Covariance between x and y.
Variance of variable x.
Variance of variable y.
Expected value of variable u.
Expected value of variable v.
Covariance between x and u.
Covariance between x and v.
Covariance between y and u.
Covariance between y and v.
Variance of variable u.
Variance of variable v.
Covariance between u and v.
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. tools:::Rd_expr_doi("10.2307/2286081")
Goodman, L. A. (1960). On the exact variance of products. Journal of the American Statistical Association, 55(292), 708. tools:::Rd_expr_doi("10.2307/2281592")