estimate_prod: Estimation of statistics computed from products of random,...

In psychmeta/psychmeta: Psychometric Meta-Analysis Toolkit

Estimation of statistics computed from products of random, normal variables

Description

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.

Usage

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
)

Arguments

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.

Value

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

References

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2281592")}

psychmeta/psychmeta documentation built on Feb. 12, 2024, 1:21 a.m.