###
Example of a joint density.
x <-
seq(0,5,0.2)
y <-
x
f <-
function(x,y){ 2*exp(-x)*exp(-2*y) }
z <-
outer(x,y,f)
par(mfrow=c(2,2))
persp(z)
persp(z,eye=c(5,-1,3))
persp(z,eye=c(-1,5,3))
persp(z,eye=c(5,5,3))
###
Example of plotting the joint normal distribution.
x <-
seq(-2,2,0.1)
y <-
seq(-2,2,0.1)
par(mfrow=c(2,2))
bvn
<- function(x,y){
mu1 <- 0
sigma1 <- 1
mu2 <- 0
sigma2 <- 1
rho <- 0
((2*pi*sigma1*sigma2*sqrt(1-rho^2))^(-1))*
exp( -(2*((1-rho^2))^(-1)) * (
(x-mu1)^2/sigma1^2 + (y-mu2)^2/sigma2^2
- ( (2*rho*(x-mu1)*(y-mu2) )/
(sigma1*sigma2) ) ) )
}
z1
<- outer(x,y,bvn)
persp(x,y,z1)
bvn
<- function(x,y){
mu1 <- 0
sigma1 <- 1
mu2 <- 0
sigma2 <- 1
rho <- 0.3
((2*pi*sigma1*sigma2*sqrt(1-rho^2))^(-1))*
exp( -(2*((1-rho^2))^(-1)) * (
(x-mu1)^2/sigma1^2 + (y-mu2)^2/sigma2^2
- ( (2*rho*(x-mu1)*(y-mu2) )/
(sigma1*sigma2) ) ) )
}
z2
<- outer(x,y,bvn)
persp(x,y,z2)
bvn
<- function(x,y){
mu1 <- 0
sigma1 <- 1
mu2 <- 0
sigma2 <- 1
rho <- 0.6
((2*pi*sigma1*sigma2*sqrt(1-rho^2))^(-1))*
exp( -(2*((1-rho^2))^(-1)) * (
(x-mu1)^2/sigma1^2 + (y-mu2)^2/sigma2^2
- ( (2*rho*(x-mu1)*(y-mu2) )/
(sigma1*sigma2) ) ) )
}
z3
<- outer(x,y,bvn)
persp(x,y,z3)
bvn
<- function(x,y){
mu1 <- 0
sigma1 <- 1
mu2 <- 0
sigma2 <- 1
rho <- -0.9
((2*pi*sigma1*sigma2*sqrt(1-rho^2))^(-1))*
exp( -(2*(1-rho^2)^(-1)) * (
(x-mu1)^2/sigma1^2 + (y-mu2)^2/sigma2^2
- ( (2*rho*(x-mu1)*(y-mu2) )/
(sigma1*sigma2) ) ) )
}
z4
<- outer(x,y,bvn)
persp(x,y,z4)
par(mfrow=c(2,2))
contour(x,y,z1)
contour(x,y,z2)
contour(x,y,z3)
contour(x,y,z4)