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; alternatively 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 $$ f(x) = \frac{1}{2\pi\sqrt{1-\rho^2}\sigma_1\sigma_2} \exp\left\{-\frac{1}{2(1-\rho^2)} \left[\left(\frac{x_1 - \mu_1}{\sigma_1}\right)^2 - 2\rho \left(\frac{x_1 - \mu_1}{\sigma_1}\right) \left(\frac{x_2 - \mu_2}{\sigma_2}\right) + \left(\frac{x_2 - \mu_2}{\sigma_2}\right)^2\right]\right\} $$

References

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

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

Examples

Run this code


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)