# BivNormal: Bivariate normal distribution In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```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

`Normal`
 ```1 2 3 4 5 6 7``` ```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) ```