library(MCMCpack)
n <- 50000
nu <- 100
sigma02 <- 50

x <- rchisq(n=n, df=nu)
x <- nu*sigma02 / x

y <- rinvgamma(n=n, nu/2, nu*sigma02/2 )

print(mean(x))
print(mean(y))
print(var(x))
print(var(y))

dx <- density(x)
dy <- density(y)

matplot( dx$x, dx$y, type="l",col="red")
matlines( dy$x, dy$y, type="l", lty=2)