Dvojrozmerné normálne rozdelenie

library(misc3d)
## Warning: package 'misc3d' was built under R version 3.6.1
library(rgl)

Vyrobíme si funkciu na výpočet hustoty dvojrozmerného normálneho rozdelenia:

hustota<-function(a=0,b=0,s1,s2,rho){
    x <- seq(-2,2, length= 40); y <- x
    f<-function (x,y){
        xoy = ((x-a)^2/s1^2 - 2 * rho * (x-a) * (y-b)/(s1*s2) + (y-b)^2/s2^2)/(2 * (1 - rho^2))
        density = exp(-xoy)/(2 * pi * s1*s2*sqrt(1 - rho^2))
        density
    }
    x<-y<-seq(-4,4,length=100)
    z<-outer(x,y,function(x,y)f(x,y))
    return(list(x=x,y=y,z=z))
}

\(\mu=(0,0)'\), \(\Sigma=I_2\)

\(\mu=(0,0)'\), \(\Sigma=\begin{bmatrix}4&0\\0&1\end{bmatrix}\)

\(\mu=(0,0)'\), \(\Sigma=\begin{bmatrix}1&0.6\\0.6&1\end{bmatrix}\)