extraDistr (version 1.8.1)

BivNormal: Bivariate normal distribution

Description

Density, distribution function and random generation for the bivariate normal distribution.

Usage

dbvnorm(x, y = NULL, mean1 = 0, mean2 = mean1, sd1 = 1, sd2 = sd1, cor = 0, log = FALSE)
rbvnorm(n, mean1 = 0, mean2 = mean1, sd1 = 1, sd2 = sd1, cor = 0)

Arguments

x, y

vectors of quantiles; alternativelly x may be a two-column matrix (or data.frame) and y may be omitted.

mean1, mean2

vectors of means.

sd1, sd2

vectors of standard deviations.

cor

vector of correlations (-1 < cor < 1).

log

logical; if TRUE, probabilities p are given as log(p).

n

number of observations. If length(n) > 1, the length is taken to be the number required.

Details

Probability density function $$ f(x) = \frac{1}{2\pi\sqrt{1-\rho^2}\sigma_1\sigma_2} \exp\left(-\frac{1}{2(1-\rho^2)} (z_1^2 - 2\rho z_1 z_2 + z_2^2)\right) $$

where $ z1 = (x1 - \mu1)/\sigma1 $ and $ z2 = (x2 - \mu2)/\sigma2 $.

References

Krishnamoorthy, K. (2006). Handbook of Statistical Distributions with Applications. Chapman & Hall/CRC

Mukhopadhyay, N. (2000). Probability and statistical inference. Chapman & Hall/CRC

See Also

Normal

Examples

y <- x <- seq(-4, 4, by = 0.25)
z <- outer(x, y, function(x, y) dbvnorm(x, y, cor = -0.75))
persp(x, y, z)

y <- x <- seq(-4, 4, by = 0.25)
z <- outer(x, y, function(x, y) dbvnorm(x, y, cor = -0.25))
persp(x, y, z)