Let two random variables
\(X \sim N(\mu_x, \sigma_x)\) and \(Y \sim N(\mu_y, \sigma_y)\)
with probability densities \(f_X\) and \(f_Y\).
The parameters of the distribution of the ratio \(Z = \frac{X}{Y}\) are:
\(\displaystyle{\beta = \frac{\mu_x}{\mu_y}}\),
\(\displaystyle{\rho = \frac{\sigma_y}{\sigma_x}}\),
\(\displaystyle{\delta_y = \frac{\sigma_y}{\mu_y}}\)
and \(\displaystyle{r = Cor(X, Y) = \frac{Cov(X, Y)}{\sigma_x \sigma_y}}\).
\(\mu_x\), \(\sigma_x\), \(\mu_y\) and \(\sigma_y\) are computed from
\(\beta\), \(\rho\) and \(\delta_y\) (by fixing arbitrarily \(\mu_x = 1\)).
If \(X\) and \(Y\) are independent, i.e. \(r=0\), two random samples
\(\left( x_1, \dots, x_n \right)\) and
\(\left( y_1, \dots, y_n \right)\) are simulated.
If \(X\) and \(Y\) are not independent,
a sample \(\left( (x_1, y_1), \dots, (x_n, y_n) \right)\)
is simpulated using MASS::mvrnorm().
Then \(\displaystyle{\left( \frac{x_1}{y_1}, \dots, \frac{x_n}{y_n} \right)}\) is returned.