Conditional distribution in a bivariate normal

X | Y = y ~ N(mu_x + rho sd_x (y - mu_y) / sd_y, sd_x sqrt(1 - rho^2)) and symmetrically for Y | X (Hedderich, Sachs & Reynarowych 2023, p. 324).

Usage

bvncnd(value, mu_x, mu_y, sd_x, sd_y, rho, given = c("y", "x"))

Arguments

value

Observed value of the conditioning variable.

mu_x, mu_y, sd_x, sd_y

Means and standard deviations.

rho

Correlation.

given

"y" or "x".

Value

Named list: mean, sd.

References

Hedderich, J., Sachs, L. & Reynarowych, Z. (2023). Applied Statistics: Methods Using R. Springer.

Examples

bvncnd(80, 170, 70, 10, 12, 0.6)
#> $mean
#> [1] 175
#> 
#> $sd
#> [1] 8
#>