BivNormal function

Bivariate normal distribution

Bivariate normal distribution

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

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)=12π1−ρ2σ1σ2exp⁡{−12(1−ρ2)[(x1−μ1σ1)2−2ρ(x1−μ1σ1)(x2−μ2σ2)+(x2−μ2σ2)2]}f(x)=1/(2∗π∗sqrt(1−ρ2)∗σ1∗σ2)∗exp(−(1/(2∗(1−ρ2)∗(((x1−μ1)/σ1)2−2∗ρ∗((x1−μ1)/σ2)∗((x2−μ2)/σ2)∗((x2−μ2)/σ2)2)))) 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\}f(x) = 1/(2*\pi*sqrt(1-\rho^2)*\sigma1*\sigma2) * exp(-(1/(2*(1-\rho^2)*(((x1-\mu1)/\sigma1)^2 - 2*\rho*((x1-\mu1)/\sigma2)*((x2-\mu2)/\sigma2) *((x2-\mu2)/\sigma2)^2))))

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)

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

extraDistr packageRead PDF manual
  • Maintainer: Tymoteusz Wolodzko
  • License: GPL-2
  • Last published: 2023-11-30

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