BivNormal: Bivariate normal distribution

In extraDistr: Additional Univariate and Multivariate Distributions

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) = 1/(2*π*sqrt(1-ρ^2)*σ1*σ2) * exp(-(1/(2*(1-ρ^2)* (((x1-μ1)/σ1)^2 - 2*ρ*((x1-μ1)/σ2)*((x2-μ2)/σ2) * ((x2-μ2)/σ2)^2))))

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)

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.